Question 306: Dual Nature of Matter and Radiation

Question

If the potential difference used to accelerate electrons is increased four times, by what factor does the de-Broglie wavelength associated with the electrons change?

Accepted Answer

For an electron accelerated through potential V, $\lambda \propto \frac{1}{\sqrt{V}}$
$$	herefore\quad\frac{\lambda_2}{\lambda_1}=\sqrt{\frac{V_1}{V_2}}$$
Given that, $\mathrm{V}_2=4 \mathrm{~V}_1$
$$	herefore\quad\lambda_2=\lambda_1 	imes \sqrt{\frac{\mathrm{V}_1}{4 \mathrm{~V}_1}}=\frac{\lambda_1}{2}$$

Answer

Wavelength increased two times

Answer

Wavelength decreased to half

Answer

Wavelength increased four times

Answer

Wavelength remains the same

Dual Nature of Matter and Radiation

If the potential difference used to accelerate electrons is increased four times, by what factor does the de-Broglie wavelength associated with the electrons change?

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