X Ray (Maximum Wavelength)

What is the cut off wavelength in an X-ray production tube if the accelerating voltage is 5 kV?

Answer

The cutoff frequency is when all the energy of the incoming electrons (e*U) is transferred to the photons (h*F). e is the electron charge, U is the accelerating Voltage, h is the plank constant, F is the frequency.

$e*U = h*F$

$F = C/\lambda$

C is the speed of light, lambda is the wavelength

$e*U = h*C/\lambda$

$\lambda = h*C/(e*U) = (6.626*10^-34)*(3*10^8)/[(1.6*10^-19)*(5*10^3)] =$

$=2.485*10^{-10} m =24.85 nm$