Question

The minimum wavelength of X-ray emitted by X-ray tube is \[0.4125\dot A\]. The accelerating voltage is
A. 30kV
B. 50kV
C. 80kV
D. 60kV

Answer 1

Hint: In the X-ray tube there are two plates at the two ends of the X-ray tube. X-rays will be produced when electrons will travel from one plate to another when both plates are separated by some voltage difference, this voltage difference is also known as accelerating voltage.

Complete answer:
Let us take a situation where an electron is moving from one plate of the X-ray tube to another plate and the plates are separated by the voltage difference of $V$.

Then the energy acquired by the electron will be $E = eV$-----equation (1),
where $e = $charge of electron, $V = $accelerating voltage.
Now when this electron will strike on the second plate then the emission of the X-rays will take place. To get the X-ray of minimum wavelength the ray must strike the second plate with its maximum energy, and the maximum energy of the X-ray will be,

$E = \dfrac{{hc}}{\lambda }$------equation (2)
Now equating equation (1) and equation (2), we get
$eV = \dfrac{{hc}}{\lambda }$
$ \Rightarrow \lambda = \dfrac{{hc}}{{eV}}$
Now putting the value of all constants, we get
$ \Rightarrow \lambda = \dfrac{{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{1.6 \times {{10}^{ - 19}} \times V}}$

Finally, we will get the formula as

$\lambda = \dfrac{{12400}}{V}\dot A$
Given, minimum wavelength= $\lambda = 0.4125\dot A$
So, putting this value in the above relation,

$0.4125\dot A = \dfrac{{12400}}{V}\dot A$
$ \Rightarrow V = \dfrac{{12400\dot A}}{{0.4125\dot A}}$
$ \Rightarrow V = 30,060V$
$ \Rightarrow V = 30KV$
Hence the minimum wavelength of X-ray emitted by an X-ray tube is \[0.4125\dot A\]. The accelerating voltage is $30KV$.

So, the correct answer is “Option A”.

Note:
From the above relation of the minimum wavelength and the voltage we see that the minimum wavelength is inversely proportional to the accelerating voltage. That means if we reduce the accelerating voltage by half than the previous value then the minimum voltage will be twice the previous value.