Concepts of Physics

IIT JEE Physics (1978 to 2018: 41 Years) Topic-wise Complete Solutions

Characteristic and Continuous X-rays

Problems from IIT JEE

Problem (IIT JEE 2008): Which of the following statements is wrong in the context of X-rays generated from a X-ray tube?

  1. Wavelength of characteristic X-rays decreases when the atomic number of the target increases.
  2. Cut-off wavelength of the continuous X-rays depends on the atomic number of the target.
  3. Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube.
  4. Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.

Solution: The frequency $\nu$ of characteristic X-rays is related to atomic number $Z$ by Moseley's law, \begin{align} \sqrt{\nu}=a(Z-b). \end{align} which gives, \begin{align} \lambda=\frac{c}{\nu}=\frac{c}{a^2(Z-b)^2}. \end{align} Thus, wavelength decreases with increase in $Z$. The cut-off wavelength of continuous X-rays corresponds to maximum energy of electron in X-ray tube. It is given by, \begin{align} hc/\lambda=eV, \end{align} where $V$ is accelerating potential. The intensity of X-rays depends on number of electrons striking the target per second, which in turn depends on electrical power given to the X-ray tube as energy of each electron is $eV$.