Question 311: Dual Nature of Matter and Radiation

Question

The kinetic energy of an electron is increased by 2 times, then the de-Broglie wavelength associated with it changes by a factor.

Accepted Answer

Kinetic Energy, $E=\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \frac{(\mathrm{mv})^2}{\mathrm{~m}}=\frac{\mathrm{p}^2}{2 \mathrm{~m}}$
$	herefore \quad \mathrm{p}=\sqrt{2 \mathrm{mE}}\quad	ext{..... (i)}$
De-Broglie wavelength,
$$\begin{aligned}
& \lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}} \quad	ext{.... [from (i)]}\
& \Rightarrow \lambda \propto \frac{1}{\sqrt{\mathrm{E}}}
\end{aligned}$$
$	herefore \quad$ When kinetic energy is increased by 2 times, $$\mathrm{E}_2=\mathrm{E}_1+2 \mathrm{E}_1=3 \mathrm{E}_1$$
$	herefore \quad \lambda$ changes by factor of $\frac{1}{\sqrt{3}}$

Answer

$\frac{1}{3}$

Answer

$\frac{1}{\sqrt{3}}$

Answer

3

Answer

$\sqrt{3}$

Dual Nature of Matter and Radiation

The kinetic energy of an electron is increased by 2 times, then the de-Broglie wavelength associated with it changes by a factor.

Choose the correct answer: