A radioactive source in the form of a metal sphere of radius 10−2 m emits beta particles (electrons) at the rate of 5×1010 particles per second. The source is electrically insulated. How long will it take (in  μs) for its potential to be raised by 2V assuming that 40% of the emitted beta particles escape from the source.

Beta particles (i.e., electrons) escaped in t seconds. η=40100×5×1010t=2×1010tTherefore, the deficiency of electrons from a conductor results  in positive charge. As 40% beta particles escape from the source, positive charge gained by source (metal sphere),  q=ne=2×1010t×1.6×10−19C=3.2×10−9  t  CDue to this charge, the potential acquired by sphere is V=14πε0qRSubstituting given values, we get2=9.0×109×3.2×10−9t10−2          or  t=11440s≃694.44  μs