Dual Nature of Radiation and Matter - Result Question 11

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11. If the momentum of electron is changed by $P$, then the de Broglie wavelength associated with it changes by $0.5 %$. The initial momentum of electron will be :

======= ####11. If the momentum of electron is changed by $P$, then the de Broglie wavelength associated with it changes by $0.5 %$. The initial momentum of electron will be :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/dual-nature-of-radiation-and-matter/dual-nature-of-radiation-and-matter—result-question-11.md (a) $200 P$

(b) $400 P$

(c) $\frac{P}{200}$

(d) $100 P$

[2012M]

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Answer:

Correct Answer: 11. (a)

Solution:

  1. (a) The de-Broglie’s wavelength associated with the moving electron $\lambda=\frac{h}{P}$

Now, according to problem

$\frac{d \lambda}{\lambda}=-\frac{d p}{P}$

$\frac{0.5}{100}=\frac{P}{P^{\prime}}$

$P^{\prime}=200 P$ 12

(b) $\lambda \propto \frac{1}{\sqrt{V}}$

$\Rightarrow \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{V_2}{V_1}}=\sqrt{\frac{100 keV}{25 keV}}=2$

$\Rightarrow \lambda_2=\frac{\lambda_1}{2}$