The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is.

Question

Accepted Answer

Four times the initial energy. For a nonrelativistic electron, de Broglie wavelength is inversely proportional to momentum, so halving the wavelength makes momentum twice as large. Since kinetic energy is proportional to momentum squared, the final energy becomes four times the initial energy, so the added energy equals three times the initial energy; among the options, the final energy is four times the initial energy.

The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is.

Solution

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