Question

${10}^{12}$ $\alpha -$ particles (nuclei of helium) accumulate every second on a neutral conductor. Calculate the amount of time $\text{(in sec)}$ in which the sphere gets charged by $1.6\mu \text{C}$.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

$\alpha -$ particle is ${\text{He}}^{2+}$ ion, means one $\alpha -$particle carries $2e$ charge.

Number of alpha particles striking on sphere is,
$n={10}^{12}\text{per sec}$.

Charge to be accumulated on sphere is,
$q=1.6\mu \text{C}=1.6\times {10}^{-6}\text{C}$

Let $t$ be the time in which the sphere gets charged by $1.6\mu \text{C}$.

Charge accumulated = Charge adding per sec $\times$ time

$q=n\left(2e\right)\times t$

$\Rightarrow 1.6\times {10}^{-6}=n(2\times 1.6\times {10}^{-19})\times t$

$\Rightarrow t=\frac{1.6\times {10}^{-6}}{{10}^{12}\times 2\times 1.6\times {10}^{-19}}(\because n={10}^{12})$

$\Rightarrow t=\frac{10}{2}=5\text{sec}$

Hence, option $\left(d\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: When one}\alpha -\text{particle falls on sphere,}\\ \text{+2e charge gets accumulated.}\end{array}$