A radioactive source, in the form of a metallic sphere of radius `10^(-2)m` emits `beta-`particles at the rate of `5xx10^(10)` particles per second. The source is electrically insulated. How long will it take for its potential to be raised by `2V`, assuming that `40%` of the emitted `beta-`particles escape the source.

Explanation

`beta`-particles i.e. electron
`V = (1)/(4pi in_(0)).(q)/(r ) = (9xx10^(9))/(10^(-2))q = 9xx10^(11)q`
`2 = 9 xx 10^(11)q`
`q = (2)/(9) xx 10^(-11)C`
where `q:` charge acquired by sphere.
Number of `beta`-particles emitted by source `= 5xx10^(10)//sec`
`40%` of this `= 0.4xx5xx10^(10)//sec = 2xx10^(10)//sec`
`q = "net"`
`(2)/(9)xx10^(-11) = 2xx10^(10)xx1.6xx10^(-19)t`
`t = (10^(-2))/(9xx1.6)`