Dual Nature Of Radiation And Matter Ques 1
1. Electrons used in an electron microscope are accelerated by a voltage of $25$ $ \mathrm{kV}$. If the voltage is increased to $100 $ $\mathrm{kV}$ then the de-Broglie wavelength associated with the electrons would
[2011]
(a) increase by $2$ times
(b) decrease by $2$ times
(c) decrease by $4$ times
(d) increase by $4$ times
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Answer:
Correct Answer: 1.(b)
Solution: (b) $ \lambda \propto \frac{1}{\sqrt{\mathrm{V}}} $
$ \Rightarrow \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{\mathrm{V}_2}{\mathrm{V}_1}}=\sqrt{\frac{100 \mathrm{keV}}{25 \mathrm{keV}}}=2 $
$ \Rightarrow \lambda_2=\frac{\lambda_1}{2}$
BETA
