Question

An $X$-ray tube produces a continuous spectrum of radiation with its short wavelength end at $0.45\, \mathring{A}$ The maximum energy of a photon in the radiation is

• A. $30.4\,keV$
• B. $27.6\,keV$
• C. $15.2\,keV$
• D. $12.8\,keV$

Answer 1

Answer: (B)

Here, $\lambda_{min}=0.45\,\mathring{A}=0.45\times10^{-10}m$
$h=6.63\times10^{-34}J\,s, c=3\times10^{8}\,m\,s^{-1}$
Maximum energy of $X$-ray photon is
$E_{max}=h\upsilon_{max}=\frac{hc}{\lambda_{min}}=\frac{6.63\times10^{-34}\times3\times10^{8}}{0.45\times10^{-10}\times1.6\times10^{-19}}eV $
$=27.6\times10^{3}\,eV=27.6\, keV$