# A radioactive source, in the form of a metallic sphere of radius 10−2 m emits β particle at the rate of…

Q:A radioactive source, in the form of a metallic sphere of radius 10−2 m emits β particle at the rate of 1011 particle per second. The source is electrically insulated. The time required for its potential to be raised by 4 V assuming 60 % of emitted β particles escape the source is

(a) 7·29 × 10−4 s

(b) 2·79 × 10−4 s

(c) 4.63 × 10−4 s

(d) 5·67 × 10−4 s

Ans: (c)

Sol: Here, r = 10-2 m , t = ? V = 4 volt.

Number of β particle escaping the sphere/sec $\displaystyle n = \frac{60}{100}\times 10^{11}$

n = 6 × 1010 C/sec

Charge on each β particle, e= 1.6 × 10-19 C

Charge acquired by the sphere in one second

q = ne = 6 × 1010×1.6 × 10-19

= 9.6 × 10-19 C

Total charge acquired Q = CV = 4 π ∈0 r (V) $\displaystyle = \frac{1}{9\times 10^9} \times 10^{-2}\times 4$ $\displaystyle Q = \frac{4}{9} \times 10^{-11} C$

Time required $\displaystyle = \frac{Q}{q}$ $\displaystyle = \frac{4}{9}\times 10^{-11}/9.6\times 10^{-9}$

= 4.63×10-4 s

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