An isolated radioactive source in the form a metal sphere of radius 1 mm undergoes β –ray decay at a constant rate of 6.25 × 1010 /sec. Assuming 70% of the emitted β –particles escape from the source, time after which potential of the sphere rises by 1 V is

V=14πε0qr⇒1=9 x 109 x n1e10-3 ⇒n1=10-39 x 109 x 1.6 x 10-19=10714.4 Since n1=70100(n) n →no.of β particles emitted ⇒n=10070 x 10714.4⇒n=1087 x 14.4For 6.25 x1010 particles → 1secFor 1087 x 14.4 particles →'t' sec ∴t=10814.4 x 76.25 x 1010=15.5 x 10-6sec=15.5 μ sec