Question

A radioactive material is in the form of a sphere whose radius is $9\times {10}^{-3}m$. If $6.25\times {10}^{12}{\beta }^{-}$ particles are emitted per second by it then in how much time will a potential of 1 volt be produced on the sphere if it is isolated?

• A. $1.1ms$
• B. ${10}^{-8}ms$
• C. $1.0\mu s$
• D. $11\mu s$

Answer 1

The correct option is C $1.0\mu s$

Charge $Q=CV=\left(4\pi {ϵ}_{0}R\right)V=\frac{9\times {10}^{-3}}{9\times {10}^9}\times 1={10}^{-12}C$

The charge emitted per second $=6.25\times {10}^{12}\times 1.6\times {10}^{-19}={10}^{-6}C$

Thus, the time for charge Q is $\frac{{10}^{-12}}{{10}^{-6}}={10}^{-6}s=1\mu s$