# How will the radiation wavelength in the X-ray tube change if the voltage is doubled?

U2 = 2 * U1.
λ2 / λ1 -?
In an X-ray tube, the electric field performs work A to move the electron: A = q * U, where q is the electron charge, U is the voltage in the X-ray tube.
Electrons knock out photons from the anode. The work of the electric field A goes to impart the energy of motion E to the photon.
The energy of a photon is determined by the formula: E = h * c / λ, where h is Planck’s constant, c is the speed of light in vacuum, λ is the wavelength of the photon.
q * U = h * c / λ.
λ = h * c / q * U.
λ1 = h * c / q * U1.
λ2 = h * c / q * U2 = h * c / q * 2 * U1.
λ2 / λ1 = h * c * q * U1 / h * c * q * 2 * U1 = 1/2.
Answer: the wavelength will decrease by 2 times: λ2 / λ1 = 1/2.

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