MCQ Questions for Class 12 Medical Physics Dual Nature Of Radiation And Matter Quiz 16

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vacuum)

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$\dfrac{1}{c} \left(\dfrac{E}{2m} \right)^{1/2}$
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$c (2mE)^{1/2}$
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$\left(\dfrac{E}{2m} \right)^{1/2}$
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$\dfrac{1}{c} \left(\dfrac{2E}{m} \right)^{1/2}$

Explanation

For electron

De - Broglie wavelength

$\lambda_c = \dfrac{h}{p}$

where p is momentum

$p = mv$

also by energy we have

$E = \dfrac{1}{2} mv^2$

$\Rightarrow E = \dfrac{1}{2} \dfrac{p^2}{m}$

$\Rightarrow p = \sqrt{2 mE}$

$\therefore \lambda_c = \dfrac{h}{\sqrt{2 mE}}$

For photon energy

$\Rightarrow E = \dfrac{hc}{\lambda}$

$\Rightarrow \lambda = \dfrac{h c}{E}$

$\therefore \dfrac{\lambda_c}{\lambda} = \dfrac{h}{\sqrt{2 mE}} \dfrac{E}{hc}$

$= \dfrac{1}{C} \sqrt{\dfrac{E}{2m}}$

option (A) is correct.

A particle moving with kinetic energy E has de Broglie wavelength

$\lambda$ . If energy

$\Delta E$ is added to its energy, the wavelength become

$\lambda /2$ . Value of

$\Delta E$ , is?

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$2E$
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$4E$
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$3E$
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$E$

Explanation

For Partial,

$\lambda=\dfrac{h}{\sqrt{2\times (K.E)\times m}}$

$\lambda \propto \dfrac{1}{\sqrt{K.E}}$

$\dfrac{\lambda_1}{\lambda_2}=\sqrt{\dfrac{(K.E)_2}{(K.E)_1}}=\sqrt{\left(\dfrac{E+\Delta E}{E}\right)}$

$\left(\dfrac{\lambda}{\lambda/2}\right)^2=\dfrac{E+\Delta E}{E}$

$4=1+\dfrac{\Delta E}{E}$

$3=\dfrac{\Delta E}{E}$

$\boxed{\Delta E=3E}$

Option (C) is correct.

CBSE Questions for Class 12 Medical Physics Dual Nature Of Radiation And Matter Quiz 16 - MCQExams.com

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Practice Class 12 Medical Physics Quiz Questions and Answers

CBSE Questions for Class 12 Medical Physics Dual Nature Of Radiation And Matter Quiz 16 - MCQExams.com

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Practice Class 12 Medical Physics Quiz Questions and Answers

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