The term atom was introduced by Dalton and is defined as the smallest particle of an element that retains all its properties and identity during a chemical reaction.

Thomson’s Model of Atom :

According to Thomson an atom is a sphere of positive charge in which the small negatively charged particles (electrons) are embedded. The number of electrons is sufficient to neutralize the positive charge.

There are three fundamental particles which constitute an atom. These are named electrons, protons and neutrons.

Rutherford’s Model of atom :

This model was based upon the results of the famous alpha-rays scattering experiment. It is also known as ‘Planetary model’ and can be summarised in following points.

(i) Most of the mass and all the positive charge of an atom are present in a very small region called the nucleus.

(ii) The magnitude of the charge on the nucleus is different in atoms of different elements.

(iii) Electrons revolve in the space around nucleus in different circular orbits and the number of electrons is equal to the number of units of positive charge in the nucleus.

Atomic number (Z)

Number of protons in the nucleus of an atom = Number of electrons in the extra nuclear part of the electrically neutral atom.

Mass number (A)

Number of protons + Number of neutrons in the nucleus of an atom.

Types of atomic species

Isotopes : Atoms of same element having same atomic number but different mass number. For example, isotopes of Hydrogen are ${}_1{}^{\mathrm{H}},{}_1^2\mathrm{H},{}_1\mathrm{H}$

Isobars: Atoms of different elements having the same mass number but different atomic number, e.g., ${}_{}^{40}{}_{18}\mathrm{Ar}{,}_{}^{40}{}_{19}{\mathrm{K}}^{40},{}_{20}\mathrm{Ca}$

Isotones: Atoms of different elements which contain the same number of neutrons. e.g., ${}_{}^{14}{}_6\mathrm{C}$, ${}_{}^{15}{}_7\mathrm{N},{}_{}^{16}{}_{8}0$

Isoelectronic Species : Atoms or ions containing the same number of electrons.

For example, ${\mathrm{N}}^{3-},{\mathrm{O}}^{2-},{\mathrm{F}}^{-},{\mathrm{Na}}^{+},{\mathrm{Mg}}^{2+},{\mathrm{Al}}^{3+}$ and $\mathrm{Ne}$, having 10 electrons each are isoelectronic

Dual nature of light

Some properties of light can be explained only by considering the wave nature (differaction and interference) while some could be explained by the particle nature (photoelectric effect).

Characteristics of a wave

Wavelength $(\lambda )$. It is the distance between any two consecutive crests or troughs. It is expressed in $\text{AA},\mathrm{m},\mathrm{cm}$, pm or $\mathrm{nm}$.. $(1\text{AA}={10}^{-10}\mathrm{m}$ or ${10}^{-8}\mathrm{cm},1\mathrm{nm}={10}^{-9}\mathrm{m},1\mathrm{pm}={10}^{-12}\mathrm{m})$.

$$ Frequency $(v)$. It is equal to number of waves passing through a point in one second. Units are hertz or ${\mathrm{s}}^{-1}(1\mathrm{Hz}=1{\mathrm{s}}^{-1})$.

Velocity (c). It is the distance travelled by the wave in one second.

Relationship between $c,v$ and $\lambda :c=v\times \lambda$.

Amplitude (a). It is the height of the crest or depth of the trough.

Wave number $(\overline{v})$. It is equal to reciprocal of wavelength $(\overline{v}=\frac{1}{\lambda })$.

Electromagnetic spectrum. It is the arrangement of electromagnetic radiations in order of increasing wavelengths :

$$ Cosmic rays $<\gamma$-rays $<X$-rays $<UV<visible<IR<Microwaves<$ Radiowaves

Planck’s quantum theory

Radiant energy is emitted or absorbed discontinuously in the form of small packets of energy called quanta.

Energy of each quantum $\mathrm{e}=\mathrm{h}v,\mathrm{h}=$ Planck’s constant $=6.626\times {10}^{-34}\mathrm{Js}$

Total energy emitted or absorbed $=\mathrm{nhv}$ ( $\mathrm{n}$ is an integer)

Photoelectric effect:

When radiation of certain minimum frequency $\left(v_0\right)$ strikes the surface of a metal, electrons are ejected.

The photoelectric effect was finally explained by Albert Einstein in the year 1905 with the help of Planck’s quantum theory. According to this theory, the energy of one quantum of radiation depends upon its frequency. Electron would be ejected only if the energy possessed by one quantum is at least sufficient to overcome the force by which the electron is held. Thus, it must have certain minimum energy which is called threshold energy or work function. Any excess energy given by the quantum would go as kinetic energy of the ejected electron. Since according to Planck’s theory, the energy possessed by a quantum is directly proportional to the frequency of the radiation used, the kinetic energy of the ejected electron is also proportional to the frequency.

According to Planck’s Theory

$$E=hv$$

If threshold frequency for a metal is $v_0$, the energy required to make the electron just free is $h{v}_0$. The kinetic energy of the ejected electron would be equal to the difference is the energy of one quantum of the radiation used and the binding energy of the electron

$$\mathrm{\Delta }\mathrm{E}=hv-h{v}_0$$

Where $\mathrm{\Delta }\mathrm{E}$ represents the kinetic energy of the ejected electron which can be equated with it’s velocity

$$\mathrm{\Delta }\mathrm{E}=1/2m{v}^2$$

or it can be written as

$$1/2m{v}^2=hv-h{v}_0$$

This concept could not be explained by the classical wave theory but the quantum theory could provide a satisfactory explanation.

Emission spectrum of Hydrogen atom

A spectrum having distinct lines was observed for hydrogen. Rydberg gave a general relation between wave number and series of integers

$$\frac{1}{\lambda }=\overline{v}=109677(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}){\mathrm{cm}}^{-1}$$

Where $109677{\mathrm{cm}}^{-1}$ is called the Rydberg constant.

Depending upon the different valves of $n_1$ and $n_2$, these spectral lines are devided into following groups (also called series). For each group of lines $n_1$ is constant and $n_2$ varies and have values $(n_1+1)$ and higher.

Series	Region	${\mathrm{n}}_1$	${\underset{―}{\mathrm{n}}}_2$
Lyman	UV	1	$2,3,\dots \dots$
Balmer	Visible	2	$3,4,\dots \dots$
Paschen	$\mathrm{IR}$	3	$4,5,\dots$
Brackett	$\mathrm{IR}$	4	$5,6,\dots$
Pfund	IR	5	$6,7,\dots \dots .$.
Humphreys	Far IR	6	$7,8,\dots \dots .$.

These spectral lines split up further in very closely spaced lines when the sample is placed in a magnetic field. This phenomenon is known as Zeeman effect.

Bohr’s Model of Atom

Niel Bohr modified Rutherford’s model by adding the concept of quantization of energy. He conceptualised that the electrons revolve around the nucleus on fixed circular paths called orbits without losing or gaining energy. These are also called energy levels or shells. The energy of different orbits in an atom in given by the expression

$$E_n=-\frac{2{\pi }^{2}m{e}^4}{n^2{h}^2}$$

For hydrogen like species (i.e. having one electron only) this expression is written as

$$E_n=-\frac{2{\pi }^2{z}^{2}m{e}^4}{n^2{h}^2}$$

Substituting the values of $m$ (mass of electron), $e$ (charge on electron) and $h$ (Planck’s constant) in the expression for hydrogen atom we get

$$\begin{array}{rlrl}& E_n=-\frac{2.178\times {10}^{-18}}{n^2}{\mathrm{Jatom}}^{-1}\text{ or }& E_n=-\frac{13.595}{n^2}\mathrm{eV}{\mathrm{atom}}^{-1}\text{ or }& E_n=-\frac{1312}{n^2}\mathrm{kJ}{\mathrm{mol}}^{-1}\end{array}$$

Radius of a Bohr orbit is given as

$$\begin{array}{rlr}& r_n=\frac{n^2{h}^2}{4{\pi }^{2}Zm{e}^2}& r_n=\frac{5.29\times {10}^{-11}{n}^2}{Z}m\end{array}$$

For the first orbit of hydrogen

$$\begin{array}{rlr}\mathrm{r}& =5.29\times {10}^{-11}\mathrm{m}& =52.9\mathrm{pm}\end{array}$$

The change in energy when an electron goes from one orbit to another is expressed as

$\mathrm{\Delta }\mathrm{E}={\mathrm{E}}_{\text{inal }}-{\mathrm{E}}_{\text{inital }}$

The energy gain or loss takes place by the absorption or emission of radiation which are related as

$$\mathrm{\Delta }\mathrm{E}=hv=\frac{hc}{\lambda }=hc\overline{v}$$

Limitations of Bohr’s Model

It could notexplain:

Line spectra of multi electron atoms

Splitting of lines in magnetic field (Zeeman effect) and in electric field (Stark effect).

Three dimensional model of atom

Significance of Negative sign in energy expression

The negative sign in the energy expression appears because the energy of a free electron at rest is taken as zero. Such an electron would be at infinite distance away from the nucleus and would not experience any force of attraction towards it. As it comes closer, it experiences stronger and stronger attractive force and its energy would decrease. Since it is less than zero, it would have negative sign. The energy of the electron would be lowest in the orbit with $n=1$ and this most stable state is known as the ground level. If the electron has to jump to the next orbit with $n=2$, some energy must be given to it to overcome the attractive force of the nucleus. Thus in the second orbit, the energy of the electron is greater than is the first. Similarly, as the electron shifts from the second to the third, fourth and so as, its energy would increase.

Dual nature of matter and de Broglie Equation

The French physicist Louis de Broglie postulated the dual nature of moving particles and showed that wavelength $(\lambda )$ of the matter wave is related to the momentum ( $p$ ) by the equation

$$\lambda =\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}}$$

Where $m=$ mass, $v=$ velocity and $h$ is Planck’s constant.

Heisenberg’s uncertainity principle - It is impossible to measure simultaneously the position and momentum of a microscopic particle with absolute accuracy. If one of them is measured with great accuracy, the other becomes less accurate. $\mathrm{\Delta }\mathrm{x}.\mathrm{\Delta }\mathrm{p}\ge \frac{\mathrm{h}}{4\pi },\mathrm{\Delta }\mathrm{x}=$ uncertainity in position

$\mathrm{\Delta }\mathrm{p}=$ uncertainity in momentum

$\mathrm{\Delta }x.m\cdot \mathrm{\Delta }V\ge \frac{h}{4\pi },\mathrm{\Delta }V=$ uncertainity in velocity

Significant only for microscopic particles

Quantum Mechanics

Quantum mechanics takes into account the dual behaviour of matter. An equation, given by Schrodinger, which has a better physical interpretation in terms of wave properties is

$$\hat{H}\psi =E\psi$$

Where $\hat{H}$ is called hamiltonian and $\mathrm{E}$ is the total energy of the electron and $\psi$ is a mathematical function, called wave function. Its square ${\psi }^2$ is proportional to the probability of finding the electron at a given point. For this reason $\psi$ is also called probability amplitude. On solving the schrodinger wave equation, three integers appear which can have only some restricted values. These integers are called quantum numbers. The three quantum numbers thus obtained are (i) the principal quantum number ( $\mathrm{n})$, (ii) the azimuthal or subsidiary quantum number (I) and (iii) the magnetic quantum number $\left({\mathrm{m}}_1\right)$. A fourth quantum number is required to describe the electronic configuration of different elements which is called the spin quantum number $\left(m_s\right)$.

Significance of Quantum Numbers

Principal Quantum Number ( $\mathrm{n}$ ) identified the main energy level to which the electron belongs. It also specifies the average distance of the electron from the nucleus. It can have any integral value greater than zero i.e., $n=1,2,3,\dots$ The various value of $n$ are sometimes also designated by the letters $K,L,M$, $\mathrm{N},\dots$

Azimuthal Quantum Number or Angular Momentum Quantum Number (I) determines the shape of an orbital and the angular momentum of an electron occupying that orbital. It can have values from 0 to $(n-1)$, each of which represents a different sub-energy level or sub-shell. These sub-shells are designated as $s,p,d,f$ according to the value of $I=0,1,2,3$ respectively. The shapes of $s,p$ and $d$ subshells are shown below.

Magnetic Quantum Number ( $m$, or $m$ ) determines the preferred orientations of orbitals in space. The permitted values for $m$ varies from - I to + lincluding zero.

Spin Quantum Number ( $s$ or $m_s$ ) arises due to the spinning of the electron about its own axis. The spin can be clockwise represented by $+1/2$ or anti-clockwise represented by $-1/2$.

Electronic Configuration of Atoms

The arrangement of electrons in various orbitals is called the electronic configuration. This arrangement is obtained on the basis of following rules, which constitute the Aufbau Principle.

(i) The minimum energy rule

A sub-shell (group of orbitals) with lower energy is filled up first before filling of the subshell with higher energy begins. In other words, the electron must occupy the subshell of the lowest energy. The order of energy can be remembered as follows :

(a) Lower the value of $(n+1)$, lower is the energy of the subshell. For one electron systems like $\mathrm{H},{\mathrm{He}}^{+},{\mathrm{Li}}^{2+}$ etc., the energy of electrons is governed only by the value of $n$ and not by $(n+l)$.

(b) If the two subshells have the some $(n+l)$ value, the one with lower $n$ value will have the lower energy. Following these points, the sequence of orbitals for filling of electrons comes out to be :

$1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f,6d,7p$ and so on.

(ii) Pauli’s Exclusion Principle

It states that no two electrons in an atom can have the same set of values of all the four quantum numbers. It can also be said that in an orbital, there can be maximum of two electrons and they should be of opposite spin.

(iii) Hund’s Rule of Maximum Multiplicity

According to this rule electron pairing in any of the $p,d$ or $f$ orbital does not occur until all the orbitals of that sub-shell are singly occupied.

Suppose in an atom, two electrons have to occupy a p-subshell which has three orbitals. $p_x,p_y$ and $p_z$ all of which are of identical energy, In such a situation, two arrangements are possible. Both the electrons may occupy the same orbital or different orbitals. The two arrangements may be represented as $p_x{}^2,p_y{}^0$, $p_z^0$ or $p_x{}^1,p_y{}^1,p_z{}^0$. In the first arrangement, the electrons are paired while in the second, they are unpaired. According to Hund’s rule, the more stable arrangement of the two is $p_x{}^1,p_y{}^1,p_z$ in which both the electrons are unpaired. Thus, if a p-subshell has three electrons, the more stable arrangement would be $p_x{}^1,p_y{}^1,p_z{}^1$ in which all the three electrons are unpaired.

Half-filled and completely filled sub-shells are more stable due to symmetry or we can say due to exchange energy. Hence the configurations ( $n-1)d^{5}n{s}^1$ and $(n-1)d^{10}n{s}^1$ are more stable than ( $n-1)d^{4}n{s}^2$ and $(n-1)d^{9}n{s}^2$ respectively. This is reflected in the configuration of elements like $\mathrm{Cr}(z=24)$ and $\mathrm{Cu}(\mathrm{z}=$ 29), whose configurations are $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}4s^1$ and $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^1$, respectively.

Solved Problems

Question 1. What is the energy of an electron $(\mathrm{m}=9.1\times {10}^{-3}\mathrm{kg})$ moving with a speed $5.0\times {10}^7$ kilometre per second?

(a) $11.4\times {10}^{-16}\mathrm{J}$

(b) $11.4\times {10}^{-10}\mathrm{J}$

(c) $22.75\times {10}^{-24}\mathrm{J}$

(d) $22.75\times {10}^{-21}\mathrm{J}$

Show Answer

Answer (b)

$\mathrm{E}=1/2\mathrm{mv}{\mathrm{v}}^2$

Given $\mathrm{v}=5.0\times {10}^7{\mathrm{kms}}^{-1}=5.0\times {10}^{10}{\mathrm{ms}}^{-1}$

Substituting the value

$\mathrm{E}=\frac{1}{2}\times 9.1\times {10}^{-3}\mathrm{kg}\times {(5.0\times {10}^{10}{\mathrm{ms}}^{-1})}^2$

$=11.4\times {10}^{-10}{\mathrm{kgm}}^2{\mathrm{s}}^{-2}$

$=11.4\times {10}^{-10}\mathrm{J}$

Question 2. What is the momentum of a particle which has a wave length of $2A^{\circ }$ ?

(a) $3.3\times {10}^{-24}\mathrm{kg}\mathrm{ms}-1$

(b) $3.3\times {10}^{-34}\mathrm{kg}\mathrm{ms}-1$

(c) $3.3\times {10}^{-26}\mathrm{kg}\mathrm{ms}-1$

(d) $13.2\times {10}^{-44}\mathrm{kg}\mathrm{ms}-1$

Show Answer

Answer (a)

Momentum $p=\frac{h}{\lambda }$

$\mathrm{h}=6.6\times {10}^{-34}{\mathrm{kgm}}^2{\mathrm{s}}^{-1}$

Given $\lambda =2\text{AA}=2\times {10}^{-10}\mathrm{m}$

Substituting the values

$p=\frac{6.6\times {10}^{-34}{\mathrm{kgm}}^2{\mathrm{s}}^{-1}}{2\times {10}^{-10}\mathrm{m}}$

$=3.3\times {10}^{-24}{\mathrm{kgms}}^{-1}$

Question 3. What is the ratio of energies of an electron is 1 st orbits of ${\mathrm{He}}^{+}$and $\mathrm{H}$ ?

(a) $1:1$

(b) $1:2$

(c) $2:1$

(d) $4:1$

Show Answer

Answer (d)

We know that

$\mathrm{En}=-\frac{1312{\mathrm{Z}}^2}{{\mathrm{n}}^2}\mathrm{kJ}{\mathrm{mol}}^{-1}$

For $\mathrm{H},\mathrm{Z}=1$ and $\mathrm{n}=1$

$E_H=-1312(1{)}^2=-1312\mathrm{kJ}{\mathrm{mol}}^{-1}$

For ${\mathrm{He}}^{+}\mathrm{Z}=2$ and $\mathrm{n}=1$

$$\begin{array}{rlr}{E}_{\mathrm{He}}=-1312(2{)}^2& =-5248\mathrm{kJ}{\mathrm{mol}}^{-1}\frac{E_{\mathrm{He}}}{E_{\mathrm{H}}}& =\frac{-5248\mathrm{kJ}{\mathrm{mol}}^{-1}}{-1312\mathrm{kJ}{\mathrm{mol}}^{-1}}=4\end{array}$$

Question 4. Radius of which orbit of ${\mathrm{He}}^{+}$is one half as that of 4 th orbit of ${\mathrm{Be}}^{3+}$ ?

(a) 1

(b) 2

(c) 6

(d) 8

Show Answer

Answer (b)

Rn $=\frac{5.29\times {10}^{-11}\times n^2}{Z}\mathrm{m}$

For ${\mathrm{He}}^{+}:\mathrm{Z}=2,\mathrm{n}=$ ?

$\mathrm{Fe}{\mathrm{Be}}^{3+}:Z=4$ and $n=4$

$(\mathrm{rn}{)}_{\mathrm{He}+}=1/2\left({\mathrm{r}}_4\right){\mathrm{Be}}^{3+}$

$\frac{5.29\times {10}^{-11}{\mathrm{xn}}^2}{2}=\frac{1}{2}\times \frac{5.29\times {10}^{-11}\times (4{)}^2}{4}$

$n^2=4$

$\mathrm{n}=2$

So 2 nd orbit of ${\mathrm{He}}^{+}$would have one half radius than that of 4 th orbit of ${\mathrm{Be}}^{3+}$.

Question 5. What are the possible values of four enantum numbers $(\mathrm{n},\mathrm{l},\mathrm{m},\mathrm{s})$ for an electron in $4\mathrm{f}$ orbital.

(a) $4,2,2,+1/2$

(b) $4,3,2,+1/2$

(c) $5,3,2,-1/2$

(d) $3,3,1,+\frac{1}{2}$

Show Answer

Answer (b)

For an electron is $4\mathrm{f}$ orbital

$\mathrm{n}=4$ and for ’ $\mathrm{f}$ ’ orbital $\mathrm{I}=3$

Possible values for $m=-3,-2,-1,0,+1,+2,+3$

and for $S=+1/2$ and $-1/2$

So out of given choices ‘b’ is the correct choice.

Question 6. What is the uncertainty in the position of a particle if the uncertainty is its momentum is $3.3\times {10}^{-2}$ $\mathrm{kg}{\mathrm{ms}}^{-1}$.

(a) $1.6\times {10}^{-35}\mathrm{m}$

(b) $3.2\times {10}^{-33}\mathrm{m}$

(c) $3.2\times {10}^{-34}\mathrm{m}$

(d) $1.6\times {10}^{-33}\mathrm{m}$

Show Answer

Answer (d)

We know that

$\mathrm{\Delta }x\mathrm{\Delta }p\ge \frac{h}{4\pi }$

or $\mathrm{\Delta }\mathrm{x}=\frac{\mathrm{h}}{4\pi \mathrm{\Delta }\mathrm{p}}$

Where $=6.62\times {10}^{-34}\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$

and $\pi =3.1416$

Substituting the values

$\mathrm{\Delta }x=\frac{6.62\times {10}^{-34}{\mathrm{kgm}}^2{\mathrm{s}}^{-1}}{4\times 3.1416\times 3.3\times {10}^{-2}{\mathrm{kgms}}^{-1}}$

$=1.6\times {10}^{-33}\mathrm{m}$

Question 7. If the energy difference between the ground state of an atom and its excited state is $3.0\times {10}^{-19}\mathrm{J}$, what is the wavelength of the photon required to produce this transition?

(a) $6.62\times {10}^{-9}\mathrm{cm}$

(b) $6.62\times {10}^{-5}\mathrm{m}$

(c) $6.62\times {10}^{-7}\mathrm{m}$

(d) $6.62\times {10}^{-7}\mathrm{cm}$

Show Answer

Answer (c)

$\lambda =\frac{\mathrm{hc}}{\mathrm{\Delta }\mathrm{E}}$

Substituting the values $\mathrm{h}=6.62\times {10}^{-34}\mathrm{Js}$

$\mathrm{c}=3\times {10}^8{\mathrm{ms}}^{-1}$

and $\mathrm{\Delta }\mathrm{E}=3\times {10}^{-19}\mathrm{J}$

$\lambda =\frac{(6.62\times {10}^{-34}\mathrm{Js})(3.0\times {10}^8{\mathrm{ms}}^{-1})}{3\times {10}^{-19}\mathrm{J}}$

$=6.62\times {10}^{-7}\mathrm{m}$

Question 8. The ionisation energy of $\mathrm{H}$-atom (in the ground state) is $\mathrm{kJ}$. The energy required for an electron to jump from 2nd to 3rd orbit will be

(a) $x/6$

(b) $5x$

(c) $7.2x$

(d) $5x/36$

Show Answer

Answer (d)

The ionisation energy in ground state is $\mathrm{kJ}$,

so the energy of 1st orbit $\left(E_1\right)=-xkJ$

Energy of 2nd orbit $\left(E_2\right)=-\frac{x}{(2{)}^2}=-\frac{x}{4}kJ$

Energy of 3rd orbit $\left(E_3\right)=-\frac{x}{(3{)}^2}=-\frac{x}{9}\mathrm{kJ}$

Energy required to jump from 2nd to 3rd orbit

is $E_3-E_2=-\frac{X}{9}-(-\frac{X}{4})$

$=\frac{x}{4}-\frac{x}{9}=\frac{5x}{36}$

Question 9. What is the de Broglie wavelength of a $66\mathrm{kg}$ man skiing down Kufri hill in Simla at $1\times {10}^3\mathrm{m}{\sec }^{-1}$ ? (Planck’s constant $=6.6\times {10}^{-34}\mathrm{Js}$ )

(a) $1\times {10}^{-36}\mathrm{m}$

(b) $1\times {10}^{-37}\mathrm{m}$

(c) $1\times {10}^{-38}\mathrm{m}$

(d) $1\times {10}^{-39}\mathrm{m}$

Show Answer

Answer (c)

$\lambda =\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{mv}}$

Given That

$\mathrm{h}=6.6\times {10}^{-34}\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$

$\mathrm{m}=66\mathrm{kg}$

$\mathrm{v}=1\times {10}^3\mathrm{m}{\sec }^{-1}$

Substituting the values

$\lambda =\frac{6.6\times {10}^{-34}}{66\times {10}^3}=1\times {10}^{-38}\mathrm{m}$

Question 10. Which of the following has more unpaired d-electrons?

(a) ${\mathrm{Fe}}^{2+}$

(b) ${\mathrm{Zn}}^{+}$

(c) ${\mathrm{Ni}}^{3+}$

(d) ${\mathrm{Cu}}^{+}$

Show Answer

Answer (a)

The electronic configurations for various species are

$Z{n}^{+}:1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{1}3d^{10}$

${\mathrm{Fe}}^{2+}:1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}3{\mathrm{p}}^{6}3{\mathrm{d}}^6$

${\mathrm{Ni}}^{3+}:1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}2{\mathrm{p}}^{6}3{\mathrm{s}}^{2}3{\mathrm{p}}^{6}3{\mathrm{d}}^7$

$C{u}^{+}:1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}$

Thus maximum number of unpaired electrons are present in ${\mathrm{Fe}}^{2+}$

Question 11. Which of the following sets of quantum numbers represents the highest energy level in an atom?

(a) $n=3,I=1,m=1,s=+1/2$

(b) $n=3,I=2,m=1,s=+1/2$

(c) $n=4,I=0,m=0,s=+1/2$

(d) $n=3,I=0,m=0,s=+1/2$

Show Answer

Answer (b)

According to $(n+I)$ rule, the energy of an orbital depends upon the sum of the values of the principal quantum number $(n)$ and the azimuthal quantum number $(I)$. Lower the value of $(n+I)$, lower is the energy. If two different orbitals have the same value of $(n+I)$, the orbital with lower value of $n$ has lower energy.

In option (a), $(\mathrm{n}+\mathrm{I})=3+1=4$

In option $(b),(n+l)=3+2=5$

In option $(\mathrm{c}),(\mathrm{n}+\mathrm{l})=4+0=4$

In option $(\mathrm{d}),(\mathrm{n}+\mathrm{I})=3+0=3$

Thus highest energy level is depicted in option (b).

Question 12. The ionisation enthalpy of hydrogen atom is $1.312\times {10}^6\mathrm{J}\mathrm{mol}$. The energy required to excite the electron in the atom from $n_1=1$ to $n_2=2$ is

(a) $8.51\times {10}^5\mathrm{J}{\mathrm{mol}}^{-}$

(b) $7.56\times {10}^5\mathrm{J}{\mathrm{mol}}^{-}$

(c) $6.56\times {10}^5\mathrm{J}\mathrm{mol}$

(d) $9.84\times {10}^5\mathrm{J}\mathrm{mol}$

Show Answer

Answer (d)

Ionisation enthalpy of hydrogen atom is $1.312\times {10}^6\mathrm{J}\mathrm{mol}$. This suggests that the energy of electron in the ground state (first orbit) is $-1.312\times {10}^6\mathrm{J}\mathrm{mol}$.

$\mathrm{\Delta }\mathrm{E}={\mathrm{E}}_2-{\mathrm{E}}_1$

$=\left(\frac{-1.312\times {10}^6}{(2{)}^2}\right)-\left(\frac{-1.312\times {10}^6}{1}\right)$

$=9.84\times {10}^5\mathrm{J}{\mathrm{mol}}^{-1}$

Correct option is (d)

Question 13. In an atom, an electron is moving with a speed of $600\mathrm{m}/\mathrm{s}$ with an accuracy of $0.005$. Certainty with which the position of an electron can be located is $(\mathrm{h}=6.6\times {10}^{-34}\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$; mass of electron $e_{\mathrm{m}}=9.1\times {10}^{-31}\mathrm{kg}$ )

(a) $1.52\times {10}^{-4}\mathrm{m}$

(b) $5.10\times {10}^{-3}\mathrm{m}$

(c) $1.92\times {10}^{-3}\mathrm{m}$

(d) $3.84\times {10}^{-3}\mathrm{m}$

Show Answer

Answer (c)

According to Heisenberg’s uncertainty principle :

$\mathrm{\Delta }\mathrm{x}\times \mathrm{m}\mathrm{\Delta }\mathrm{v}=\frac{\mathrm{h}}{4\pi }$

$\mathrm{\Delta }\mathrm{x}=\frac{\mathrm{h}}{4\pi \mathrm{m}\mathrm{\Delta }\mathrm{V}}$ $\mathrm{\Delta }\mathrm{V}=\frac{0.005}{100}\times 600=0.03$

$\mathrm{\Delta }\mathrm{x}=\frac{6.6\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 0.03}$

$=1.92\times {10}^{-3}\mathrm{m}$

Correctoption is (c)

Question 14. Ionisation energy of ${\mathrm{He}}^{+}$is $19.6\times {10}^{-18}{\mathrm{J}}^{-{\mathrm{at}}^{-1}}$. The energy of the stationary state $(\mathrm{n}=1)$ of ${\mathrm{Li}}^{2+}$ is

(a) $4.41\times {10}^{-16}{\mathrm{Jatom}}^{-1}$

(b) $-2.2\times {10}^{-15}{\mathrm{Jatom}}^{-1}$

(c) $-4.41\times {10}^{-17}{\mathrm{Jatom}}^{-1}$

(d) $-8.82\times {10}^{-17}{\mathrm{Jatom}}^{-1}$

Show Answer

Answer (c)

$\mathrm{IE}=-{\mathrm{E}}_1$

$\frac{{\left(E_1\right)}_{\text{Het }}}{{\left(E_1\right)}_{i+}^{2_i^{+}}}=\frac{{\left(Z_{\text{Het }}\right)}^2}{{\left(Z_{\mathrm{Li}}^{+2}\right)}^2}$

$\frac{-19.6\times {10}^{-18}}{{\left(E_1\right)}_{Li}^{2+}}=\frac{{\left(Z_{\text{Het }}\right)}^2}{{\left(Z_{\mathrm{Li}}{}^2\right)}^2}$

$\frac{-19.6\times {10}^{-18}}{{\left(E_1\right)}_{\mathrm{Li}}{}^{2+}}=\frac{4}{9}$

$\mathrm{Or}{\left(E_1\right)}_{L_i}{}^{2+}=\frac{-19.6\times {10}^{-18}\times 9}{4}$

$=-4.41\times {10}^{-17}{\mathrm{Jatom}}^{-1}$

Correct option is (c)

Question 15. A gas absorbs a photon of $355\mathrm{nm}$ and emits at two wavelengths. If one of the emission is at 680 $\mathrm{nm}$, the other is at

(a) $1035\mathrm{nm}$

(b) $743\mathrm{nm}$

(c) $325\mathrm{nm}$

(d) $518\mathrm{nm}$

Show Answer

Answer (b)

$\frac{hc}{\lambda }=\frac{hc}{{\lambda }_1}+\frac{hc}{{\lambda }_2}$

Or $\frac{1}{\lambda }=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$

$\frac{1}{355}=\frac{1}{680}+\frac{1}{{\lambda }_2}$

Or $\frac{1}{{\lambda }_2}=\frac{1}{355}-\frac{1}{680}$

$=\frac{680-355}{680\times 355}$

$=1.346\times {10}^{-3}$

Or ${\lambda }_2=743\mathrm{nm}$

PRACTICE QUESTIONS

1. Rutherford’s experiment on scattering of $\alpha$-particles showed for the first time that the atom has

(a) electrons

(b) protons

(b) nucleus

(d) neutrons

Show Answer

Answer: (c)

2. The increasing order [lowest first] for the values of $\mathrm{e}/\mathrm{m}$ [charge / mass] for electron [e], proton $[p]$, neutron $[n]$ and alpha particles $[\alpha ]$ is

(a) $e,p,n,\alpha$

(b) $n,p,e,\alpha$

(c) $n,p,\alpha ,e$

(d) $n,\alpha ,p,e$

Show Answer

Answer: (d)

3. Bohr’s model can explain

(a) the spectrum of hydrogen atom only

(b) spectrum of atom or ion containing one electron only

(c) the spectrum of hydrogen molecule

(d) the solar spectrum

Show Answer

Answer: (a)

4. Rutherford’s alpha particle scattering experiment eventually led to the conclusion that

(a) mass and energy are related

(b) electrons occupy space around the nucleus

(c) neutrons are buried deep in the nucleus

(d) the point of impact with matter can be precisely determined

Show Answer

Answer: (b)

5. The wavelength of the electron emitted, when in a hydrogen atom, electron falls from infinity to stationary state 1 , would be [Rydberg’s constant $=1.097\times {10}^7{\mathrm{m}}^{-1}$ ]

(a) $91\mathrm{nm}$

(b) $192\mathrm{nm}$

(c) $406\mathrm{nm}$

(d) $9.1\times {10}^{-8}\mathrm{nm}$

Show Answer

Answer: (a)

6. The shortest wavelength in hydrogen spectrum of lyman series, when $R_H=109678{\mathrm{cm}}^{-1}$ is

(a) $1002.7\text{AA}$

(b) $1215.67\text{AA}$

(c) $1127.30\text{AA}$

(d) $911.7\text{AA}$

Show Answer

Answer: (d)

7. The wave number of the spectral line in the emission spectrum of hydrogen will be equal to $8/9$ times the Rydberg’s constant if the electron jumps from

(a) $n=3$ to $n=1$

(b) $n=10$ to $n=1$

(c) $n=9$ to $n=1$

(d) $n=2$ ton $=1$

Show Answer

Answer: (a)

8. Those species are called isotones which have same

(a) atomic number

(b) mass number

(c) number of electrons

(d) number of neutrons

Show Answer

Answer: (d)

9. Calculate the wavelength of the light required to break the bond between two chlorine atoms in a chlorine molecule. The $\mathrm{Cl}-\mathrm{Cl}$ bond energy is $243\mathrm{kJ}{\mathrm{mol}}^{-1}$

(a) $8.18\times {10}^{-31}\mathrm{m}$

(b) $6.26\times {10}^{-21}\mathrm{m}$

(c) $4.91\times {10}^{-7}\mathrm{m}$

(d) $4.11\times {10}^{-6}\mathrm{m}$

Show Answer

Answer: (c)

10. A $600\mathrm{W}$ mercury lamp emits monochromatic radiation of wavelength $3.315\times {10}^{-7}\mathrm{m}$. How many photons are emitted from the lamp per second?

(a) $1\times {10}^9$

(b) $1\times {10}^{20}$

(c) $1\times {10}^{21}$

(d) $1\times {10}^{23}$

Show Answer

Answer: (c)

11. Photoelectric emission is observed from a metal surface with incident frequencies $v_1$ and $v_2$ where $v_1>v_2$ If the kinetic energies of the photoelectrons emitted in the two cases are in the ration $2:1$, then the threshold frequency $v_0$ of the metal is

(a) $v_1-v_2$

(b) $\frac{v_1-v_2}{h}$

(c) $2v_1-v_2$

(d) $2v_2-v_1$

Show Answer

Answer: (d)

12. The ratio of the energy of a photon of $2000\text{AA}\text{AA}$ wavelength radiation to that of $4000\text{AA}$ radiation is

(a) $1/4$

(b) 4

(c) $1/2$

(d) 2

Show Answer

Answer: (d)

13. Atom of an element has $Z$ electrons and its atomic mass is $2Z+3$. The number of neutrons in its nucleus will be

(a) $2Z$

(b) $\mathrm{Z}+3$

(c) $Z+2$

(d) $\mathrm{Z}$

Show Answer

Answer: (b)

14. If an isotope of hydrogen has two neutrons in its atom, its atomic number and mass number will be

(a) 2 and 1

(b) 3 and 1

(c) 1 and 1

(d) 1 and 3

Show Answer

Answer: (d)

15. The triad of nuclei that is isotonic is

(a) ${}_6^{14}\mathrm{C},{}_7^{15}\mathrm{N},{}_9^{17}\mathrm{F}$

(b) ${}_6^{12}\mathrm{C},{}_7^{14}\mathrm{N},{}_9^{19}\mathrm{F}$

(c) ${}_6^{14}\mathrm{C},{}_7^{14}\mathrm{N},{}_9^{17}\mathrm{F}$

(d) ${}_6^{14}\mathrm{C},{}_7^{14}\mathrm{N},{}_9^{19}\mathrm{F}$

Show Answer

Answer: (a)

16. Which of the following is deflected most under the effect of electric field ?

(a) $\alpha$-rays

(b) $\beta$-rays

(c) $\gamma$-rays

(d) X-rays

Show Answer

Answer: (b)

17. The frequency of light having wavelength $500\mathrm{nm}$ is

(a) $5\times {10}^{15}\mathrm{Hz}$

(b) $5\times {10}^{10}\mathrm{MHZ}$

(c) $2\times {10}^{-15}\mathrm{Hz}$

(d) $6\times {10}^{14}\mathrm{Hz}$

Show Answer

Answer: (d)

18. The ionization energy of ${\mathrm{He}}^{+}$is $19.6\times {10}^{-18}\mathrm{J}/$ atom. The energy of the first stationary state of ${\mathrm{Li}}^{+2}$ is

(a) $-2.18\times {10}^{-18}\mathrm{J}/$ atom

(b) $-4.90\times {10}^{-18}\mathrm{J}/$ atom

(c) $+4.90\times {10}^{-18}\mathrm{J}/$ atom

(d) $+4.41\times {10}^{-17}\mathrm{J}/$ atom

Show Answer

Answer: (d)

19. The energy of an electron in the first orbit of hydrogen is $-13.6\mathrm{eV}$. Which one of the following is the second excited state of electron in hydrogen atom?

(a) $-3.4\mathrm{eV}$

(b) $-6.8\mathrm{eV}$

(c) $-1.5\mathrm{eV}$

(d) $+3.4\mathrm{eV}$

Show Answer

Answer: (c)

20. The wave number of the radiation emitted when the electron jumps from fourth energy level to second energy level in ${\mathrm{He}}^{+}$is about

(a) $20565{\mathrm{cm}}^{-1}$

(b) $41030{\mathrm{cm}}^{-1}$

(c) $82258{\mathrm{cm}}^{-1}$

(d) $5141{\mathrm{cm}}^{-1}$

Show Answer

Answer: (a)

21. The energy of the second Bohr’s orbit of the hydrogen atom is $-328\mathrm{kJ}{\mathrm{mol}}^{-1}$. The energy of fourth Bohr’s orbit would be

(a) $-1312\mathrm{kJ}{\mathrm{mol}}^{-1}$

(b) $-164\mathrm{kJ}{\mathrm{mol}}^{-1}$

(c) $-82\mathrm{kJ}{\mathrm{mol}}^{-1}$

(d) $-41\mathrm{kJ}{\mathrm{mol}}^{-1}$

Show Answer

Answer: (c)

22. The threshold frequency of a metal is $1\times {10}^{15}{\mathrm{s}}^{-1}$. The ratio of maximum kinetic energies of the photoelectrons when the metal is irradiated with radiations of frequencies $1.5\times {10}^{15}{\mathrm{s}}^{-1}$ and $2.0\mathrm{x}$ ${10}^{15}{\mathrm{s}}^{-1}$ respectively, would be

(a) $3:4$

(b) $1:2$

(c) $2:1$

(d) $4:3$

Show Answer

Answer: (b)

23. The threshold frequency of a metal ’ $M$ ’ is $1.5\times {10}^{15}{\mathrm{s}}^{-1}$. The maximum K.E. of the photoelectrons, when the metal is irradiated with radiations of frequency $2.5\times {10}^{15}{\mathrm{s}}^{-1}$, would be

(a) $6.63\times {10}^{-20}\mathrm{J}$

(b) $1.0\times {10}^{-19}\mathrm{J}$

(c) $6.63\times {10}^{-19}\mathrm{J}$

(d) $1.0\times {10}^{-18}\mathrm{J}$

Show Answer

Answer: (c)

24. The de-Broglie wavelength associated with a body of mass $1000\mathrm{g}$ moving with a velocity 100 ${\mathrm{ms}}^{-1}$ is

(a) $6.62\times {10}^{-39}\mathrm{m}$

(b) $6.62\times {10}^{36}\mathrm{cm}$

(c) $6.62\times {10}^{-36}\mathrm{m}$

(d) $3.31\times {10}^{-32}\mathrm{m}$

Show Answer

Answer: (c)

25. The H-specturm shows

(a) Heisenberg’s uncertainity principle

(b) diffraction

(c) polarisation

(d) presence of quantized energy levels

Show Answer

Answer: (d)

26. Correct set of four quantum numbers for the valence (outermost) electron of rubidium ( $Z=37)$ is

(a) $5,0,0,+\frac{1}{2}$

(b) $5,1,0,+\frac{1}{2}$

(c) $5,1,1,+\frac{1}{2}$

(d) $6,0,0,+\frac{1}{2}$

Show Answer

Answer: (a)

27. The principal quantum number of an orbital is related to the

(a) size of the orbital

(b) spin angular momentum

(c) orientation of the orbital in space

(d) orbital angular momentum

Show Answer

Answer: (a)

28. Which one of the following sets of quantum numbers represents an impossible arrangement?

$\begin{array}{cccccclcl}& & n& & 1& & m& & s\\ \text{(a)}& & 3& & 2& & -2& & \frac{1}{2}\\ \text{(b)}& & 4& & 0& & 0& & \frac{1}{2}\\ \text{(c)}& & 3& & 2& & -3& & \frac{1}{2}\\ \text{(d)}& & 5& & 3& & 0& & -\frac{1}{2}\end{array}$

Show Answer

Answer: (c)

29. Which of the following has the maximum number of unpaired electrons?

(a) ${\mathrm{Mg}}^{2+}$

(b) ${\mathrm{Ti}}^{3+}$

(c) ${\mathrm{V}}^{3+}$

(d) ${\mathrm{Fe}}^{2+}$

Show Answer

Answer: (d)

30. The number of nodal planes in a $p_x$ orbital is

(a) one

(b) two

(c) three

(d) zero

Show Answer

Answer: (d)

31. The electrons, identified by quantum numbers $n$ and $I$, (i) $n=4,I=1$, (ii) $n=4,I=0$, (iii) $n=3,I=2$, and (iv) $n=3,I=I$ can be placed in order of increasing energy, from the lowest to highest, as

(a) (iv) $<$ (ii) $<$ (iii) $<$ (i)

(b) (ii) $<$ (iv) $<$ (i) $<$ (iii)

(c) (i) $<$ (iii) $<$ (ii) $<$ (iv)

(d) (iii) $<$ (i) $<$ (iv) $<$ (ii)

Show Answer

Answer: (a)

32. The orbital angular momentum of an electron is 2 s orbital is

(a) $+\frac{1}{2}\frac{h}{2\pi }$

(b) zero

(c) $\frac{h}{2\pi }$

(d) $\sqrt{2}\cdot \frac{h}{2\pi }$

Show Answer

Answer: (b)

33. The number of radial nodes in $3s$ and $2p$ orbitals, respectively are

(a) 2 and 0

(b) 0 and 2

(c) 1 and 2

(d) 2 and 1

Show Answer

Answer: (a)

34. The correct set of quantum numbers for the unpaired electron of chlorine atom is

$\begin{array}{llllcccccc}& n& 1& m& & & & n& 1& m\\ \text{(a)}& 2& 1& 0& & & \text{(b)}& 2& 1& 1\\ \text{(c)}& 3& 1& 1& & & \text{(d)}& 3& 0& 0\end{array}$

Show Answer

Answer: (c)

35. Maximum number of electrons in a subshell of an atom is determined by the following

(a) $21+1$

(b) $41-2$

(c) $2n^2$

(d) $41+2$

Show Answer

Answer: (d)

36. What is the maximum number of electrons that can be associated with the following set of quantum numbers $\mathrm{n}=2,\mathrm{I}=0,\mathrm{m}=0$

(a) 10

(b) 6

(c) 4

(d) 2

Show Answer

Answer: (d)

37. The following quantum number are possible for how many orbitals? $n=3,I=2,m=+2$

(a) 1

(b) 2

(c) 3

(d) 4

Show Answer

Answer: (a)

38. If $n=3,I=0,m=0$, then atomic number is

(a) 12,13

(b) 13,14

(c) 10,11

(d) 11,12

Show Answer

Answer: (d)

39. The number of electrons is an atom with atomic number 105 having $(\mathrm{n}+\mathrm{I})=8$ is

(a) 15

(b) 17

(c) 19

(d) 21

Show Answer

Answer: (b)

40. Which of the following set of quantum numbers is not possible?

(a) $n=3,I=2,m=0,s=-1/2$

(b) $n=3,I=2,m=-2,s=-1/2$

(c) $n=3,I=3,m=-3,s=+\frac{1}{2}$

(d) $n=3,I=1,m=0,s=+1/2$

Show Answer

Answer: (c)

41. According to Bohr’s theory, angular momentum for an electron is 5th orbit is:

(a) $\frac{5\mathrm{h}}{\pi }$

(b) $\frac{2.5\mathrm{h}}{\pi }$

(c) $\frac{5}{\mathrm{h}}$

(d) $\frac{25h}{\pi }$

Show Answer

Answer: (b)

42. A5f orbital has

(a) one node

(b) two nodes

(c) threenodes

(d) four nodes

Show Answer

Answer: (d)

43. The azimuthal quantum number for 17 th electron of $\mathrm{Cl}$ atom is

(a) 1

(b) 2

(c) 3

(d) 0

Show Answer

Answer: (a)

44. If electronic structure of oxygen atom is written as $1s^{1}2s^2$ , if would violate

(a) Hund’s rule

(b) Pauli’s exclusion principle

(c) both a and b

(d) none of the above

Show Answer

Answer: (a)

45. With increase in principal quantum number ( $\mathrm{n}$ ), the energy difference between adjacent energy levels in hydrogen atom

(a) increases

(b) decreases

(c) remains contant

(d) decreases for lower values of $n$ and increases for higher values of $n$

Show Answer

Answer: (b)

46. The de-Broglie wavelength of an electron which has kinetic energy of $2.14\times {10}^{-22}\mathrm{J}$ would be $({\mathrm{m}}_{\mathrm{e}}$ $=9.1\times {10}^{-31}\mathrm{kg}$ )

(a) $9.3\times {10}^{-4}\mathrm{m}$

(b) $9.3\times {10}^{-7}\mathrm{m}$

(c) $9.3\times {10}^{-8}\mathrm{m}$

(d) $9.3\times {10}^{-10}\mathrm{m}$

Show Answer

Answer: (c)

47. The nineteenth electron of chromium has which of the following set of quantum numbers?

(a) $3,0,0,1/2$

(b) $3,2,-2,1/2$

(c) $4,0,0,1/2$

(d) $4,1,-1,\frac{1}{2}$

Show Answer

Answer: (c)

48. Which of the following statements is true for chloride ion and potassium ion, which are iso electronic?

(a) The have same size

(b) chloride ion is bigger than potassium ion

(c) Potassium ion is bigger than chloride ion

(d) Size of an ion depends on the other cation or anion present

Show Answer

Answer: (b)

49. The configuration $1s^2,2s^2,2p^{5}3s^1$ represents

(a) Ground state of ${\mathrm{N}}^{3-}$

(b) Ground state of $F$

(c) Excited state of ${\mathrm{O}}_2^{-}$

(d) Excited state of neon

Show Answer

Answer: (d)

50. The ground state electronic configuration of chromium is

(a) $[\mathrm{Ar}]3{\mathrm{d}}^{5}4{\mathrm{s}}^1$

(b) $[\mathrm{Ar}]3{\mathrm{d}}^{4}4{\mathrm{s}}^2$

(c) $[\mathrm{Ar}]3{\mathrm{d}}^{6}4{\mathrm{s}}^0$

(d) $[\mathrm{Ar}]4{\mathrm{d}}^{5}4{\mathrm{s}}^1$

Show Answer

Answer: (a)

51. What will be the uncertainty in the momentum of an electron if uncertainty in its position is zero

(a) Zero

(b) $\ge \frac{h}{4\pi }$

(c) $<\frac{h}{4\pi }$

(d) infinite

Show Answer

Answer: (d)

52. The electrons distribute themselves to retain similar spins as far as possible in a set of degenerate orbitals. This statement relates to

(a) Pauli’s Exclusion Principle

(b) Law of degeneration

(c) Hurd’s Rule

(d) Aufbau Principle

Show Answer

Answer: (c)

53. The electron with which of the following values of quantum numbers is expected to possess highest energy

(a) $3,2,2,1/2$

(b) $4,2,0,1/2$

(c) $4,1,0,-1/2$

(d) $5,0,0,1/2$

Show Answer

Answer: (b)

54. An electron with $+1\frac{1}{2}$ value for spin quantum number and -1 value for magnetic quantum number can not be present in

(a) s-orbital

(b) p-orbital

(c) d-orbital

(d) f-orbital

Show Answer

Answer: (a)

55. The maximum number of electrons that can be accommodated in a subshell is given by

(a) $21+1$

(b) $4I+2$

(c) $2n^2$

(d) $2I+2$

Show Answer

Answer: (b)

56. The ratio of ionization energy of $\mathrm{H}$ and ${\mathrm{Be}}^{3+}$ is

(a) $1:1$

(b) $1:3$

(c) $1:9$

(d) $1:16$

Show Answer

Answer: (d)

57. The electrons present in $\mathrm{K}$ shell of any atom will differ in value of which quantum number

(a) Value of $n$

(b) Value of $\mathrm{I}$

(c) Value of $m$

(d) Value of $m_s$

Show Answer

Answer: (d)

58. Cathode rays are

(a) Stream of electrons

(b) Stream of $\propto$-particles

(c) Coloured radiations

(d) Electromagnetic radiations

Show Answer

Answer: (a)

59. The de-Broglie wavelength for particles having same kinetic energy is

(a) Independent of its velocity

(b) Directly proportional to its velocity

(c) Inversely proportional to its velocity

(d) Unpredictable

Show Answer

Answer: (b)

60. The electron level which allows hydrogen to absorb photons but not to emit is

(a) $1\mathrm{s}$

(b) $2\mathrm{s}$

(c) $2\mathrm{p}$

(d) 3 d

Show Answer

Answer: (a)

61. Which of the following ions has the maximum magnetic moment?

(a) ${\mathrm{Mn}}^{2+}$

(b) ${\mathrm{Ti}}^{2+}$

(c) ${\mathrm{Fe}}^{2+}$

(d) ${\mathrm{Cr}}^{2+}$

Show Answer

Answer: (a)

62. In Balmer series of lines of Hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of Hydrogen?

(a) $2\to 5$

(b) $2\to 3$

(c) $5\to 2$

(d) $3\to 2$

Show Answer

Answer: (c)

63. In a multi electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic field?

(i) $n=1,I=0,m=0$

(ii) $\mathrm{n}=2,\mathrm{I}=1,\mathrm{m}=1$

(iii) $\mathrm{n}=2,\mathrm{I}=0,\mathrm{m}=0$

(iv) $\mathrm{n}=3,\mathrm{I}=2,\mathrm{m}=0$

(v) $n=3,I=2,m=1$

(a) (i) and (ii)

(b) (ii) and (iii)

(c) (iii) and (iv)

(d) (iv) and (v)

Show Answer

Answer: (d)

64. The uncertainties in the velocity of two particles $A$ and $B$ are 0.05 and $0.02{\mathrm{ms}}^{-1}$ respectively. The mass of $B$ is five times to that of $A$. The ratio of uncertainties in their positions is :

(a) 2

(b) 0.25

(c) 4

(d) 1

Show Answer

Answer: (a)

65. What is the lowest energy of the spectral line emitted by the hydrogen atom in the Lyman series? ( $\mathrm{h}=$ Planck’s constant, $\mathrm{c}=$ velocity of light, $\mathrm{R}=$ Rydberg’s constant)

(a) $\frac{5\mathrm{hcR}}{36}$

(b) $\frac{4\mathrm{hcR}}{3}$

(c) $\frac{3\mathrm{hcR}}{4}$

(d) $\frac{7\mathrm{hcR}}{144}$

Show Answer

Answer: (c)

66. Calculate the wavelength (in nanometer) associated with a proton moving at $1.0\times {10}^3{\mathrm{ms}}^{-1}$. (mass of proton $=1.67\times {10}^{-27}\mathrm{kg}$ and $\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js}$ )

(a) $0.032\mathrm{nm}$

(b) $0.40\mathrm{nm}$

(c) $2.5\mathrm{nm}$

(d) $14.0\mathrm{nm}$

Show Answer

Answer: (b)

67. The energy required to break one mole of $\mathrm{Cl}-\mathrm{Cl}$ bonds in ${\mathrm{Cl}}_2$ is $242\mathrm{kJ}{\mathrm{mol}}^{-1}$. The longest wavelength of light capable of breaking a single $\mathrm{Cl}-\mathrm{Cl}$ bond is

(a) $594\mathrm{nm}$

(b) $640\mathrm{nm}$

(c) $700\mathrm{nm}$

(d) $494\mathrm{nm}$

Show Answer

Answer: (d)

68. The frequency of light emitted for the transition $\mathrm{n}=4$ to $\mathrm{n}=2$ of ${\mathrm{He}}^{+}$is equal to the transition in $\mathrm{H}$ atom corresponding to which of the following?

(a) $n=2$ to $n=1$

(b) $n=4$ to $n=3$

(c) $n=3$ to $n=2$

(d) $n=3$ to $n=1$

Show Answer

Answer: (a)

69. Which of the following statements is correct for an electron that has the quantum numbers $n=4$ and $m=-2$ ?

(a) the electron may be in d orbital.

(b) the electron may be in $p$ orbital

(c) the electron is in the second principal shell.

(d) the electron must have a spin $+\frac{1}{2}$.

Show Answer

Answer: (a)

70. Energy of an electron is given by

$E=-2.178\times {10}^{-18}\mathrm{J}\left(\frac{Z^2}{n^2}\right)$

Wavelength of light required to excite an electron in an Hydrogen atom from level $n=1$ to $n=2$ will be

$(\mathrm{h}=6.62\times {10}^{-34}\mathrm{Js}\text{ and }\mathrm{c}=3\times {10}^8{\mathrm{ms}}^{-1})$

(a) $1.214\times {10}^{-7}\mathrm{m}$

(b) $2.186\times {10}^{-7}\mathrm{m}$

(c) $6.500\times {10}^{-7}\mathrm{m}$

(d) $8.500\times {10}^{-7}\mathrm{m}$

Show Answer

Answer: (a)