Question

A copper sphere of mass $2.0g$ contains about $2\times 10^{22}$ atoms. The charge on the nucleus of each atom is $29e$ $(e=$ electronic charge). The mass of an electron is $9.11\times 10^{-31}kg.$ How much mass will the sphere lose or gain if it is a given a charge of $+2\mu C$ ?

• A. Loss a mass of $1.13\times 10^{-14}g$
• B. Gain a mass of $1.13\times 10^{-14}g$
• C. Neither gain nor lose any mass
• D. Change in mass will depend upon the kinetic energy of the electrons

Answer 1

Answer: (A)

To give positive charge to the copper sphere, a certain number of free electrons must be removed.-
The total number of electrons is $29\left(2\times 10^{22}\right)$ $=5.8\times 10^{23}$
Since a positive charge of $2\mu C$ is to be given, the number of electrons to be removed $\frac{2\times 10^{-6}}{1.6\times 10^{-19}}=1.25\times 10^{13}$
The mass of the electrons removed
$=1.25\times 10^{13}\times 0.91\times 10^{-30}kg$
$=1.13\times 10^{-17}kg=1.13\times 10^{-14}kg$
This mass will be lost by the copper sphere.