Question

The operating voltage in the Coolidge tube is ${10^5}\,V$ . The speed of X-Rays produced is ________ $m{s^{ - 1}}$
A) $2 \times {10^8}$
B) ${10^6}$
C) ${10^5}$
D) $3 \times {10^8}$

Answer 1

To solve the question, the thing you need to know is that X-rays will be generated when the electrons hit the anode, and the operating voltage would only affect when they hit with what energy, but doesn’t play any role in deciding the speed of X-Rays. The question is only trying to confuse you since X-rays would travel with the same speed as they normally do.

Complete step by step solution:
As explained in the hint section of the solution to the asked question, the operating voltage of the Coolidge tube only affects the electrons, the time at which they will strike the anode, or hit the anode, and the energy with which they will do so. But conceptually, operating voltage has no role to play in deciding the speed at which X-Rays would travel after being produced. Although yes, the operating voltage will be the major deciding factor behind the time at which the electrons will strike the anode since it will decide the speed at which the electrons will travel inside the tube from one point to another, but once the electrons have hit the anode, it will lose all the credibility in deciding the speed of the X-rays produced.

Now, we know that X-Ray is nothing but an electromagnetic wave, and as we know, electromagnetic waves travel with the speed of light in vacuum, given by the constant $c$ which is numerically equal to:
$c = 3 \times {10^8}\,m{s^{ - 1}}$

Hence, the X-Rays produced will also travel with the speed of light. Thus, we can see and safely say that the option (D) is the correct answer to the asked question.

Note: Many students try to find the energy provided by the operating voltage using the formula $E = eV$ and then equate it with the kinetic energy, but they forget that this process is only valid for finding the speed of electrons travelling in the tube and not for the speed of X-Rays produced. X-rays will only travel with the speed of light, no matter what is the operating voltage of the Coolidge tube.