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Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would:

1. increase by 2 times
2. decrease by 2 times
3. decrease by 4 times
4. increase by 4 times

Correct answer: decrease by 4 times

Solution

The de-Broglie wavelength is inversely proportional to the square root of the accelerating voltage. Increasing the voltage from 25 kV to 100 kV (a factor of 4) reduces the wavelength by a factor of √4 = 2. Thus, the wavelength decreases by 2 times.

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