Question

It has been given that the power of an X-ray tube is $16W$. Assume that the potential difference applied across the tube is $5kV$, then what will be the number of electrons striking the target per second?
$\begin{aligned} & A.8.4\times {{10}^{16}} \\\ & B.5\times {{10}^{17}} \\\ & C.2\times {{10}^{16}} \\\ & D.2\times {{10}^{19}} \\\ \end{aligned}$

Answer 1

The energy developed in the tube can be found by taking the product of the power of the tube and the time taken. The power generated per unit second will be the energy of the tube. Energy can also be found by taking the product of the electronic charge and the electric potential. Take the ratio of both these values of energies which will give the number of electrons generated per second. This all will help you in solving this answer.

Complete step by step answer:
The power generated per unit second will be the energy of the tube. That is, as the power generated is given as $16W$, then the energy developed in unit second will be,
$E=16J$
The potential difference across the tube will be given as,
$P.D=5kV$
The energy of one electron which is being accelerated at this given value of potential can be shown as,
$E=eV$
Substituting the values in it will give,
$E=eV=1.6\times {{10}^{-19}}\times 5\times {{10}^{3}}=8\times {{10}^{-16}}J$
The number of electrons per second will be the ratio of these two energies. That is we can write that,
$n=\dfrac{16}{8\times {{10}^{-16}}}=2\times {{10}^{16}}\text{electrons}$
Hence the number of electrons per second has been obtained.
This is mentioned in the question as option C.

Note:
Power is defined as the measure of energy converted or transferred in a unit time. The unit of power is the watt, in the international system of units. This will be equivalent to one joule in a second. In some situations the power is being mentioned as the activity.