Question

A copper sphere of mass $2.0 g$ contains about $2 \times 10^{22}$ atoms. The charge on the nucleus of each atom is $29 e$ $(e=$ 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.