Question

In a certain particle accelerator, electrons emerge in pulses at the rate of 250 pulses per second. Each pulse is of duration of 200 ns and the electrons in the pulse constitute a current of 250 mA. The number of electrons delivered by the accelerator per pulse is
A) $8.00 \times {10^{10}}$
B) $5.00 \times {10^{10}}$
C) $3.13 \times {10^{10}}$
D) $9.60 \times {10^{10}}$

Answer 1

Hint:This question is from electricity. The problem is solved by the Electric Current concept. Apply the Electric Current equation to find the number of electrons delivered by the accelerator per pulse.


Formula used:
i) $I = \dfrac{q}{t}$
Where,
I = Current
q = Charge
t = time
ii) $n = \dfrac{q}{e}$
Where,
n = Number of electrons
q = Charge
e = Charge of an electron


Complete answer:
$I = \dfrac{q}{t}$
I = 25 mA = 0.25 A
t = 200 ns = $2 \times {10^{ - 7}}s$
The charge in a pulse will be,
$q = It$
$q = 0.25 \times 2 \times {10^{ - 7}} = 5 \times {10^{ - 8}}C$
The number of electrons delivered by the accelerator per pulse is given below.
$n = \dfrac{q}{e}$
$n = \dfrac{{5 \times {{10}^8}}}{{1.6 \times {{10}^{ - 19}}}} = 3.13 \times {10^{11}}$

Hence, the correct option is Option C) $3.13 \times {10^{10}}$.

Additional Information:
The electric current is a flow of charged particles (electrons) through wires and other components.
Electric current is the rate of flow of charge.
Electric current flows from the negative terminal of the cell to the positive terminal.
The conventional direction of electric current is taken as opposite to the direction of the flow of charge (electrons).


Note: The S.I unit of charge is coulomb and the S.I unit of electric current is ampere (coulomb per second).