A radioactive source in the form of a metallic sphere of radius 2 cm emits β - particles at the rate of 2×1010 particles per second. The source is electrically insulated. How long will it take for its potential to be raised by 5 V. Assuming that 50% of emitted β-particle escapes the source.
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a
2.25×10−2s
b
0.69×10−2s
c
4.25×10−2s
d
3.25×10−2s
answer is B.
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Detailed Solution
Total charge emitted=q=efficiency ×No of particles per sec×charge on one particle×time ⇒q=50100×2×1010×1.6×10−19×t ⇒q=1.6×10−9t Potential at surface of sphere =V=kqR ⇒5=9×109×1.6×10−9t2×10−2 ⇒t=0.69×10−2s