Question

In X-ray tubes the potential difference between the anode and the cathode is 20kV and the current flowing is 1.6mA. The number of electrons striking the anode in 1s is ___________. $\text{(Charge of an electron = 1}\text{.6}\times \text{1}{{\text{0}}^{-19}}C)$
A. $\text{1}{{\text{0}}^{14}}$
B. $\text{1}\text{.25}\times \text{1}{{\text{0}}^{16}}$
C. $\text{1}{{\text{0}}^{16}}$
D. $\text{6}\text{.25}\times \text{1}{{\text{0}}^{18}}$

Answer 1

Hint: We can simply calculate this problem by using the charge of an electron and the amount of current flowing through the X-ray tube. In an X-ray tube, the electrons will flow from cathode to anode and there are no other loads.

Formula used:
$i=ne$, where n is the number of electrons and e is the charge of the electron.

Complete step by step answer:
We can write the given information from the question.
Current flowing through the tube can be written as,
$i=1.6mA$
The potential difference between the anode and cathode can be written as,
$V=20kV$
The current flowing through the X-ray tube can be written as,
$i=ne$, where n is the number of electrons and e is the charge of the electron.
Here we have to find the number of electrons striking the anode in 1 second.
Therefore, the number of electrons will be,
$n=\dfrac{i}{e}$
We can assign the given details to the equation.
$n=\dfrac{1.6\times {{10}^{-3}}}{1.6\times {{10}^{-19}}}={{10}^{16}}$
Therefore, the correct option is C.

Additional information:
X-ray tubes working with the acceleration and deceleration of electrons. So the change in kinetic energy will provide energy to the X-rays. It mainly consists of cathode, anode, and glass envelope. This glass envelope can sustain a huge amount of heat and it allows to maintain the vacuum condition. Normally it is made up of Pyrex glass. As we know, the cathode is a negatively charged electrode and the anode is a positively charged electrode. We will keep X-ray tubes in a lead-lined protective housing. It can prevent excessive exposure of X-rays and mechanical strength to the X-ray tube. Even though the X-rays are made with the electron, it does not contain any electrons. Therefore, it cannot be deflected by the electric and magnetic fields.

Note: In some questions, additional information will confuse candidates. So it is better to choose the required quantities for the calculations. Here we are calculating the number of charges in 1 second. That’s why it is not mentioned in the ratio. Otherwise, we have to consider that also to find the number of electrons. Do not forget to make the quantities in SI units, otherwise, the powers will be different and will provide the wrong answer.