Through what potential difference δv must electrons be accelerated (from rest) so that they will have the same wavelength as an x-ray of wavelength 0.150 nm ? use 6.63×10−34 j⋅s for planck's constant, 9.11×10−31 kg for the mass of an electron, and 1.60×10−19 c for the charge on an electron. express your answer using three significant figures.

66.3 V

Explanation:

The wavelength of the electron must be equal to that of the x-ray photon:

the De Broglie wavelength of the electron is related to its momentum, p, by the formula

where h is the Planck constant. Solving the formula, we find

Now we can find the electron's energy using the formula

Then, we know that the energy of an electron accelerated through a potential difference of is

where

is the electron charge

Solving the equation for the potential difference, we find

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