A neutral sphere is bombarded with 10^{12} , | vedclass

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Question

(A) The number of $\alpha$-particles falling on the sphere in $t$ seconds is $N = 10^{12}t$.Each $\alpha$-particle carries a charge of $q_{\alpha} = +

Vedclass · Accepted Answer

$6.25$

Vedclass · Answer

(A) The number of $\alpha$-particles falling on the sphere in $t$ seconds is $N = 10^{12}t$.Each $\alpha$-particle carries a charge of $q_{\alpha} = +2e$,where $e = 1.6 	imes 10^{-19} \, C$.The total charge $Q$ accumulated in time $t$ is given by $Q = N 	imes q_{\alpha} = (10^{12}t) 	imes (2e)$.Given $Q = 2 \, \mu C = 2 	imes 10^{-6} \, C$.Equating the values: $2 	imes 10^{-6} = 10^{12} 	imes t 	imes 2 	imes 1.6 	imes 10^{-19}$.$2 	imes 10^{-6} = 3.2 	imes 10^{-7} 	imes t$.$t = \frac{2 	imes 10^{-6}}{3.2 	imes 10^{-7}} = \frac{20}{3.2} = 6.25 \, s$.

$A$ neutral sphere is bombarded with $10^{12} \, \alpha$-particles per second. How much time in seconds will it take to accumulate a charge of $2 \, \mu C$?

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