Question

The electric current in an X-ray tube (from the target to the filament) operating at 40 kV is 10 mA. Assume that on an average, 1% of the total kinetic energy of the electron hitting hte target are converted into X-rays.
(a) What is the total power emitted as X-rays and (b) how much heat is produced in the target every second?

Answer 1

Given:
V = 30 KV
i = 10mA

1% of T_KE (total kinetic energy) = X-ray
i = ne
$$\begin{gathered} \mathrm{or}n=\frac{{10}^{-2}}{1.6\times {10}^{-19}} \\ =0.625\times {10}^{17}(\mathrm{number}\mathrm{of}\mathrm{electrons}) \end{gathered}$$


KE of one electron = eV
$$\begin{gathered} =1.6\times {10}^{-19}\times 40\times {10}^3 \\ =6.4\times {10}^{-15}\mathrm{J} \\ {\mathrm{T}}_{\mathrm{KE}}=0.625\times 6.4\times {10}^{17}\times {10}^{-15} \\ =4\times {10}^2\mathrm{J} \end{gathered}$$
(b) Heat produced in target per second = 400 − 4 = 396 J