Question

An X-ray tube operated at $50kW$, produces heat at the target at the rate of $796W$. If 0.5% of the energy of electrons is used for X-ray generation, what is the number of electrons striking the target per second?

• A. ${10}^{19}$
• B. ${10}^{18}$
• C. ${10}^{17}$
• D. ${10}^{16}$

Answer 1

The correct option is C ${10}^{17}$

Given that $0.5$% of the energy is used for generating X-rays.

$\Rightarrow 99.5$% is generated out as heat.

Therefore, $VI\times 0.995=796W$ and $V=50kV$

We can write the current as $I=ne$ where $n$ is the no. of electrons striking the target per second and $e$ is the charge of the electron.

Thus, $50\times {10}^3\times n\times 1.6\times {10}^{-19}\times 0.995=796$

$\Rightarrow n=\frac{796}{50\times 1.6\times 0.995}\times {10}^{16}={10}^{17}$