First slide

X-rays

Question

If a voltage applied to an X-ray tube is increased to 1.5 times the minimum wavelength ( $λ_{\min}$ ) of at X-ray continuous spectrum shifts by $Δλ$ = 26 pm. The initial voltage applied to the tube is

Moderate

A

$\approx$ 10 kV
B

$\approx$ 16 kV
C

$\approx$ 50 kV
D

$\approx$ 75 kV

Solution

$\begin{array}{l} λ_{\min} = \frac{hc}{eV} \Rightarrow λ_{1} \frac{hc}{{eV}_{1}} and λ_{2} = \frac{hc}{{eV}_{2}} \\ ∴ Δλ = λ_{2} - λ_{1} = \frac{hc}{e} [\frac{1}{V_{2}} - \frac{1}{V_{1}}] . Given V_{2} = 1 .5 V_{1} \\ on solving we get V_{1} = 16000 volt = 16 kV . \end{array}$

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