physics-class-12-unit-12-chapter-05-problem-solving-session-structure-of-atom-l-5-9-iy1x9f9wwpu

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Charge and Mass of Subatomic Particles </primary>
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| Name     | Symbol | Absolute charge/C          |  Relative charge | Mass/kg                    | Mass/u   | Approx. mass/u |
| -------- | -------| --------                   | --------         | --------                   | -------- |----------      |
|Electron  | $e$    |$-1.602176 \times 10^{-19}$ |$-1$              |$9.109382 \times 10^{-31}$  | $0.00054$|   $0$          |
| Proton   | $p$    |$+1.602176 \times 10^{-19}$ |$+1$              |$1.6726216 \times 10^{-27}$ | $1.00727$|   $1$          |
| Neutron  | $n$    | $0$                        |$0$               |$1.674927 \times 10^{-27}$  | $1.00867$|   $1$          |

- Calculate the mass and charge of one mole of electrons.
- Find (a) the total number and (b) the total mass of protons in $34 \mathrm{mg}$ of $\mathrm{NH}_3$ at STP.

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<footer style = "font-size: 18px"> $\rightarrow$ Problem Solving Session Structure of Atom $\rightarrow$ <span style = "color:blue"> Charge and Mass of Subatomic Particles </span> $\rightarrow$ Charge and Mass of Subatomic Particles $\rightarrow$ Charge and Mass of Subatomic Particles </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Charge and Mass of Subatomic Particles </primary>
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- **(b)**

- ${NH}_3 {A}=179$

- 179 of ${NH}_3  6.023 \times 10^{23} {NH}_3$ molecules

- 34 {mg } of ${NH}_3  \frac{6.023 \times 10^{23}}{17 \times 10^3} \times 34=12.046 \times 10^{20} {NH}_3 $ molecules

- ${NH}_3 \Rightarrow 10  { protons } \Rightarrow 34 { mg} { NH_3} \Rightarrow 1.2046 \times 10^{22} \text { protons } $

-  Mass of proton =$1.2046 \times 10^{22} \times 1.672 \times 10^{-27} \{kg} $ = 20.1  mg

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<footer style = "font-size: 18px">Charge and Mass of Subatomic Particles $\rightarrow$ Charge and Mass of Subatomic Particles $\rightarrow$ <span style = "color:blue"> Charge and Mass of Subatomic Particles </span> $\rightarrow$ Atomoic Mass and Atomic Number $\rightarrow$ Atomoic Mass and Atomic Number </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Atomoic Mass and Atomic Number </primary>
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- <span style="color:green">$_z^AX$</span>

- How many neutrons and protons are there in ${ }_{26}^{56} \mathrm{Fe}$ ?
- An ion with mass number 37 possesses one unit of negative charge. If the ion contains $11.1$percent more neutrons than the electrons, find the symbol of the ion.

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<footer style = "font-size: 18px">Charge and Mass of Subatomic Particles $\rightarrow$ Charge and Mass of Subatomic Particles $\rightarrow$ <span style = "color:blue"> Atomoic Mass and Atomic Number </span> $\rightarrow$ Atomoic Mass and Atomic Number $\rightarrow$ Atomoic Mass and Atomic Number </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Wavelength - Wavenumber-Frequency-Time Period-Energy </primary>
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- Find energy of each of the photons which

-    (i) Correspond to light of frequency $3 \times 10^{15} \mathrm{Hz}$.
  
-    (ii) Have wavelength of $0.50 \mathring{A} $.
   
- Find the wavelength of the photon whose period is $2.0 \times 10^{-10} \mathrm{~s}$.

- $E=.h \nu=\frac{h c}{\lambda}=h c \bar{\nu}=\frac{h}{\tau}$

- $\nu=\frac{c}{\lambda}=c \bar{\nu}=\frac{1}{\tau}$

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<footer style = "font-size: 18px">Atomoic Mass and Atomic Number $\rightarrow$ Atomoic Mass and Atomic Number $\rightarrow$ <span style = "color:blue"> Wavelength - Wavenumber-Frequency-Time Period-Energy </span> $\rightarrow$ Wavelength - Wavenumber-Frequency-Time Period-Energy $\rightarrow$ Wavelength - Wavenumber-Frequency-Time Period-Energy </footer>

- (a) - (i)
- $\nu=3 \times 10^{15} \mathrm{ ~ Hz} \Rightarrow E=h \nu$

- $=6.626 \times 10^{-34} {J} { s}  3\times 10^{15}{s}^{+} $

- $=19.88 \times 10^{-19} \mathrm{ ~ J}$
- (ii)

- $\lambda=0.5 \mathring{A}=5 \times 10^{-11} { m}$

- $E=\frac{h c}{\lambda}=\frac{6.626 \times 10^{-34} \times 3 \times 10^8 .{Js}  {ms^+}}{5 \times 10^{-11} { m}}=3.976 \times 10^{-15} \mathrm{ ~ J}$

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<footer style = "font-size: 18px">Atomoic Mass and Atomic Number $\rightarrow$ Wavelength - Wavenumber-Frequency-Time Period-Energy $\rightarrow$ <span style = "color:blue"> Wavelength - Wavenumber-Frequency-Time Period-Energy </span> $\rightarrow$ Wavelength - Wavenumber-Frequency-Time Period-Energy $\rightarrow$ Photoelectric Effect </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Photoelectric Effect </primary>
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- A photon of wavelength $4 \times 10^{-7} \mathrm{~ m}$ strikes on metal surface, the work function of the metal being $2.13 \mathrm{eV}$. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron.  $(\left.1 \mathrm{eV}=1.6020 \times 10^{-19} \mathrm{~ J}\right)$.

- $ \lambda=4 \times 10^{-7} \mathrm{~ m} $

- $ \phi_0=2.13 \mathrm{~ eV}$

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<footer style = "font-size: 18px">Wavelength - Wavenumber-Frequency-Time Period-Energy $\rightarrow$ Wavelength - Wavenumber-Frequency-Time Period-Energy $\rightarrow$ <span style = "color:blue"> Photoelectric Effect </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Hydrogen Atom Energy Levels </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Photoelectric Effect </primary>
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- (i) $E=\frac{h c}{\lambda} =\frac{6.626 \times 10^{-34} \times 3 \times 10^8 \mathrm{Js ~ ms}^{-1}}{4 \times 10^{-7} \mathrm{~ m}} =4.07 \times 10^{-19} \mathrm{~ J}$

- = $\frac{4.07 \times 10^{-19}}{1.602 \times 10^{-19}} {eV}=3.10{eV}$

- (ii) $e_{K E}=E-\phi_0=0.97 \mathrm{~ eV}$

- (iii) $\frac{1}{2} m v^2=0.97 \times 1.602 \times 10^{-19} \mathrm{~ J} $

- $v^2=\frac{2 \times 0.97 \times 1.602 \times 10^{-19}}{9.11 \times 10^{-31}} \mathrm{\frac{J}{Kg}} m^2 s^{-2} $

- $v=5.84 \times 10^6 \mathrm{~ ms}^{-1}$

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<footer style = "font-size: 18px">Wavelength - Wavenumber-Frequency-Time Period-Energy $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Photoelectric Effect </span> $\rightarrow$ Hydrogen Atom Energy Levels $\rightarrow$ Hydrogen Atom Energy Levels </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Hydrogen Atom Energy Levels </primary>
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- What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with $n=4$ to an energy level with $n=2$ ?
- How much energy is required to ionise a $\mathrm{H}$ atom if the electron occupies $n=4$ orbit?

- $n = 4 $
- $n = 3 $
- $n = 2 $
- $n = 1 $

- $E_n=-2.18 \times 10^{-18}\left(\frac{Z^2}{n^2}\right) \mathrm{J}$

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<footer style = "font-size: 18px">Photoelectric Effect $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Hydrogen Atom Energy Levels </span> $\rightarrow$ Hydrogen Atom Energy Levels $\rightarrow$ Hydrogen Atom Energy Levels </footer>

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### <primary style="font-size:24px"> Hydrogen-like Systems </primary>
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- **Calculate the energy required for the following process**

- $\mathrm {He}^+ (\mathrm {g}) \rightarrow \mathrm {H}e^{2+}(\mathrm {g}) + \mathrm {e}^-$

- $E_n=-2.18 \times 10^{-18}\left(\frac{Z^2}{n^2}\right) \mathrm{J}$

- $\mathrm{E} = -2.18\times 10 ^{-18} \times 4 \mathrm {J}$

- $ = \underbrace{-8.72 \times 10 ^{-18}} \mathrm {J}$

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<footer style = "font-size: 18px">Hydrogen Atom Energy Levels $\rightarrow$ Hydrogen Atom Energy Levels $\rightarrow$ <span style = "color:blue"> Hydrogen-like Systems </span> $\rightarrow$ de-Brogile's Hypothesis $\rightarrow$ Quantum Numbers </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> de-Brogile's Hypothesis </primary>
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- The mass of an electron is $9.1\times 10^{-31}\mathrm { kg.}$ If its $\mathrm {K.E.}$ is $3.0 \times 10 ^{-25} \mathrm { J}$, calculate its wavelength.

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

- $ {K E}= \frac{p^2}{2 m}=3 \times 10^{-25} \mathrm{ J} $

- $ p^2=2 \times 9.11 \times 10^{-31} \times 3 \times 10^{-25} \mathrm { J}  \mathrm {~ kg}$

- ${p}=7.39 \times 10^{-28} \mathrm{~ kg} \mathrm{~ m} \mathrm{~ s}^{-1}$

- $ \lambda=\frac{h}{p} =\frac{6.626 \times 10^{-34} \mathrm{Js}}{7.39 \times 10^{-28} {kg} { m} \mathrm{~ s}^{-1}} = 0.897 \times 10^{-6} {m} = 897 {nm}$

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<footer style = "font-size: 18px">Hydrogen Atom Energy Levels $\rightarrow$ Hydrogen-like Systems $\rightarrow$ <span style = "color:blue"> de-Brogile's Hypothesis </span> $\rightarrow$ Quantum Numbers $\rightarrow$ Quantum Numbers </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Quantum Numbers </primary>
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- How many subshells are associated with $n=4?$ 
- How many electrons will be present in the subshells having $m_s$ value of $-1 / 2$ for $n=4 ?$

- $n=1,2,3, \cdots $

- $ l=0,1,2, \cdots, n-1 $

- $m_l=-l,-l+1, \cdots, l-1, l $

- $ m_s= \pm 1 / 2$

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<footer style = "font-size: 18px">Hydrogen-like Systems $\rightarrow$ de-Brogile's Hypothesis $\rightarrow$ <span style = "color:blue"> Quantum Numbers </span> $\rightarrow$ Quantum Numbers $\rightarrow$ Electronic Configuration </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Electronic Configuration </primary>
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- An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the electronic configuration of the element.

- $\underline{\text{ Increasing order of} ~n +l :}$

- $1 s$ $2s$ $2 p$ $3 s$ $3 p$ $4 s$ $3 d$ $4 p$ $5 s \ldots$.

- $\text { Number of } p=29=z \quad \mathrm{Cu}$

- ${ }_{29}^{64} \mathrm{Cu} \quad 1 s^2 \quad {2 s^2} \quad {2 p^6} \quad 3 s^2 \quad3 p^6 \quad 4 s \quad 3d$

- $\underbrace{4s^2 \quad 3d^9} $

- $4s^1 \quad 3d^{10}$

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<footer style = "font-size: 18px">Quantum Numbers $\rightarrow$ Quantum Numbers $\rightarrow$ <span style = "color:blue"> Electronic Configuration </span> $\rightarrow$ Nodes in Orbitals $\rightarrow$ Nodes in Orbitals </footer>

### <Success style="font-size:25px"> Problem Solving Session Structure Of Atom L-5 </Success>
### <primary style="font-size:24px"> Nodes in Orbitals </primary>
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- Arrange the following orbitals in increasing order of radial nodes, angular nodes, and total nodes:

- 1s, 2s, 2p, 3s, 3p, 3d

- number of radial nodes $=n-1-1$

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<footer style = "font-size: 18px">Quantum Numbers $\rightarrow$ Electronic Configuration $\rightarrow$ <span style = "color:blue"> Nodes in Orbitals </span> $\rightarrow$ Nodes in Orbitals $\rightarrow$ Effective Nuclear Charge </footer>

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### <primary style="font-size:24px"> Effective Nuclear Charge </primary>
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- Among the following pairs of orbitals which orbital will experience the larger effective nuclear charge?

- (i) $1 \mathrm{~ s}$ and $2 \mathrm{~ s}$,

- (ii) 4d and 4f,

- (iii) 3d and 3p.

- $ 1 s>2 s$

- $ 4 d>4 f $

- $ 3 p>3 d$

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<footer style = "font-size: 18px">Nodes in Orbitals $\rightarrow$ Nodes in Orbitals $\rightarrow$ <span style = "color:blue"> Effective Nuclear Charge </span> $\rightarrow$ Thank You $\rightarrow$  </footer>