Question

An 𝑋-ray tube produces a continuous spectrum of radiation with its short wavelength end at $0.45\stackrel{\circ }{A}$. What is the maximum energy of a photon in the radiation?

B) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at $0.45\stackrel{\circ }{A}$ with maximum energy of a photon in the radiation being $27.6\text{keV}$. Guess what order of accelerating voltage (for electrons) is required in such a tube?

Answer 1

A) Given,
Wavelength $\left({\lambda }_{min}\right)=0.45\stackrel{\circ }{A}$
Maximum energy of a photon :
$E=\frac{hc}{{\lambda }_{min}}$
$h=6.63\times {10}^{-34}Js$
$c=3\times {10}^{8}m/s$
$E=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{0.45\times {10}^{-10}\times 1.6\times {10}^{-19}}$
$E=27,625eV$
$E=27.6\text{keV}$
Final Answer : $27.6\text{keV}$

B) Incident electron should have at least $27.6\text{keV}$ energy to get a X-ray of $27.6\text{keV}$. Therefore, the accelerating voltage of the order of $30\text{keV}$ is required for producing X-rays.
Final Answer: order of $30kV$