First slide

X-rays

Question

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

Easy

A

>124 kv
B

<124 kV
C

between 60 kV and 70 kV
D

= 100 kv

Solution

From conservation of energy the electron kinetic energy equals the maximum photon energy (we neglect the work function Φ because it is normally so small compared to ${eV}_{o}$ ).
$\begin{array}{l} {eV}_{o} = {hv}_{\max} \\ or {eV}_{o} = \frac{hc}{λ_{\min}} \\ ∴ V_{o} = \frac{hc}{{eλ}_{\min}} or \\ V_{o} = \frac{12400 \times 10^{- 10}}{10^{- 11}} = 124 kV \end{array}$
Hence, accelerating voltage for electrons tn X-ray machine should be less than 124 kV.

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