A copper sphere whose radius is 108 cm has a very thin surfa

A copper sphere whose radius is 1.08 cm has a very thin surface coating of nickel. Some of the nickel atoms are radioactive, each atom emmiting an electron as it decays. Half of these electrons enter the copper sphere, each deposting 100 keV of energy there. The other half of the electron escape, each carying aeay a charge of -e. The nickel coating has an activity of 10.0 mCi (=10.0 millicuries = 3.70 x10^8 radioactive decays per second). The sphere is hung from a long, nonconducting string and insulated from its surrondings. How long will it take for the potential of the sphere to increase by 1000 V?

Solution

the charge is calculated as follows:

       q = V*R/k = 1000*1.08*10^-2 / 9*10^9 = 1.2x10^-9 C

Number of electrons:

      n = q/e = 1.2x10^-9 / 1.6x10^-19 = 7.5x10^9 electrons

the time t is calculated as follows:

     t = (1/2)(7.5x10^9 / 3.70 x10^8 ) = 10.13 s