If a voltage applied to an X - ray tube is increased to 1.5 times… - Vidyadip

MCQ

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

A
$\approx 10\, kV$
✓
$\approx 16\, kV$
C
$\approx 50\, kV$
D
$\approx 75\, kV$

✓

Answer

Correct option: B.

$\approx 16\, kV$

b
(b) ${\lambda _{\min }} = \frac{{hc}}{{eV}}$ $⇒$ ${\lambda _1} = \frac{{hc}}{{e{V_1}}}$and ${\lambda _2} = \frac{{hc}}{{e{V_2}}}$
$\therefore$ $\Delta \lambda = {\lambda _2} - {\lambda _1} = \frac{{hc}}{e}\left[ {\frac{1}{{{V_2}}} - \frac{1}{{{V_1}}}} \right]$. Given $V_2\, = 1.5\, V_1$
on solving we get $V_1\, =\, 16000\, volt \, = \,16\, kV$.

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