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.

Question

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.

Infinity Learn · Accepted Answer

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 $$=V=kqR$$ ⇒$$5=9$$×$$109$$×$$1.6$$×$$10$$−$$9t2$$×$$10$$−$$2$$ ⇒$$t=0.69$$×$$10$$−$$2s$$

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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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