Question

The potential difference in an X -ray tube is 5 kV and the current through it is 3.2 mA. Then the number of the electrons striking the target per second is

• A. $2\times {10}^{16}$
  
• B. $5\times {10}^{16}$
  
• C. $1\times {10}^{16}$
  
• D. $4\times {10}^{16}$

Answer 1

The correct option is A

$2\times {10}^{16}$

Let 'n' be the number of electrons hitting the target. Let 't' be the total time the X-ray tube was in working condition.
If 'I' is the current throught the tube, and 'e' is the charge on one electron, then
$I\frac{q}{t}$ Where 'q' is the total charge hitting the target in the given time.
$q=n\times e$
$\Rightarrow I=\frac{n\times e}{t}$
Hence, $\frac{n}{t}=\frac{I}{e}=\frac{3.2\times {10}^{-3}}{-1.6\times {10}^{-19}}$ (Charge on one electron is $1.6\times {10}^{-19}C$ )
$=2\times {10}^{16}$......(We ignore the negative charge of an electron and only consider the magnitude to find the number of electrons)

$\frac{n}{t}$ gives us the rate at which the electrons strike the target, which is equal to the number of electrons striking the target in one second.

Hence, the number of electrons striking the target in one second is $2\times {10}^{16}$