Dual Nature of Radiation and Matter - Result Question 11
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 :
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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 :
c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) $200 P$
(b) $400 P$
(c) $\frac{P}{200}$
(d) $100 P$
[2012M]
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Answer:
Correct Answer: 11. (a)
Solution:
- (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) $\lambda \propto \frac{1}{\sqrt{V}}$
$\Rightarrow \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{V_2}{V_1}}=\sqrt{\frac{100 keV}{25 keV}}=2$
$\Rightarrow \lambda_2=\frac{\lambda_1}{2}$
