Q139 / 200 · JIPMER 2008 · Physics

Hard $X$-rays for the study of fractures in bones should have a minimum wavelength of $10^{-11} \mathrm{~m}$. The accelerating voltage for electrons in $X$-ray machine should be

  • Correct answer
    A
    $ \lt 124 \mathrm{kV}$
  • B
    $\gt 124 kV$
  • C
    between 60 kV and 70 kV
  • D
    $=100 \mathrm{kV}$

Solution

From conservation of energy the kinetic energy of electron equals the maximum photon energy (we neglect the work function $\phi$ because it is normally so small compared to $e V_0$ ). $\therefore \quad e V_0=h v_{\max }$ or $e V_0=\frac{h c}{\lambda_{\min }}$ $\therefore \quad V_0=\frac{h c}{e \lambda_{\min }}$ or $\begin{aligned} V_0 & =\frac{12400 \times 10^{-10}}{10^{-11}} \\ & =124 \mathrm{kV}\end{aligned}$ Hence, accelerating voltage for electrons in $X$-ray machine should be less than 124 kV .

Hence, the correct answer is option: 'A'.

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