SATHEE: Modern Physics 1 Question 31

Modern Physics 1 Question 31

28. In a $C O$ molecule, the distance between $C$ (mass $= 12 a m u$ ) and $O$ $($ mass $= 16 a m u)$ , where $1 a m u = \frac{5}{3} \times 10^{- 27} k g$ , is close to

(a) $2.4 \times 10^{- 10} m$

(b) $1.9 \times 10^{- 10} m$

(d) $4.4 \times 10^{- 11} m$

(2010)

Passage 2

When a particle is restricted to move along $x$ -axis between $x = 0$ and $x = a$ , where $a$ is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends $x = 0$ and $x = a$ . The wavelength of this standing wave is related to the linear momentum $p$ of the particle according to the de-Broglie relation. The energy of the particle of mass $m$ is related to its linear momentum as $E = \frac{p^{2}}{2 m}$ . Thus, the energy of the particle can be denoted by a quantum number $n$ taking values $1, 2, 3, \dots (n = 1$ , called the ground state) corresponding to the number of loops in the standing wave.

Use the model described above to answer the following three questions for a particle moving in the line $x = 0$ to $x = a$ . [Take $h = 6.6 \times 10^{- 34} J s$ and $e = 1.6 \times 10^{- 19} C$ ]

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Solution:

$I = μ r^{2}$ ( where, $μ =$ reduced mass)

$μ = \frac{m_{1} m_{2}}{m_{1} + m_{2}} = \frac{48}{7} a m u = 11.43 \times 10^{- 27} k g$

Substituting in $I = μ r^{2}$ we get,

$\begin{aligned} r & = \sqrt{\frac{I}{μ}} = \sqrt{\frac{1.87 \times 10^{- 46}}{11.43 \times 10^{- 27}}} \\ = 1.28 \times 10^{- 10} m \end{aligned}$

Modern Physics 1 Question 31

28. In a $C O$ molecule, the distance between $C$ (mass $= 12 a m u$ ) and $O$ $($ mass $= 16 a m u)$ , where $1 a m u = \frac{5}{3} \times 10^{- 27} k g$ , is close to

Passage 2

Solution:

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Modern Physics 1 Question 31

28. In a CO molecule, the distance between C (mass =12amu ) and O ( mass =16amu), where 1amu=53×10−27kg, is close to

Passage 2

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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28. In a $C O$ molecule, the distance between $C$ (mass $= 12 a m u$ ) and $O$ $($ mass $= 16 a m u)$ , where $1 a m u = \frac{5}{3} \times 10^{- 27} k g$ , is close to