MP Board · Class 12 · Physics · Dual Nature of Radiation and MatterHow does the de Broglie wavelength of an electron depend on the accelerating potential \( V \)?
Step-by-Step Solution
The de Broglie wavelength of an electron accelerated through a potential difference ( V ) is inversely proportional to the square root of the accelerating potential. The mathematical relation is given by ( \lambda = \frac{12.27}{\sqrt{V}} \text{ \AA} ). As the accelerating potential increases, the velocity of the electron increases, its momentum increases, and consequently its de Broglie wavelength decreases significantly.
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