Question 344: Dual Nature of Matter and Radiation

Question

If the kinetic energy of a free electron doubles, it's de Broglie wavelength ($$\lambda$$) changes by a factor

Accepted Answer

$$\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$$ where $$\mathrm{E}$$ is the K.E.
$$\begin{aligned}
& 	herefore \lambda \propto \frac{1}{\sqrt{\mathrm{E}}} \quad 	herefore \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{\mathrm{E}_1}{\mathrm{E}_2}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}} \
& 	herefore \lambda_2=\frac{\lambda_1}{\sqrt{2}}
\end{aligned}$$
Thus $$\lambda$$ charges by a factor $$\frac{1}{\sqrt{2}}$$

Answer

$$\frac{1}{\sqrt{2}}$$

Answer

$$\frac{1}{2}$$

Answer

$$\sqrt{2}$$

Answer

$$2$$

Dual Nature of Matter and Radiation

If the kinetic energy of a free electron doubles, it's de Broglie wavelength ($\lambda$) changes by a factor

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