Question

An electron and a proton are at a distance of \[{\rm{1}}\mathop {\rm{A}}\limits^{\rm{0}} \]. Then find the dipole moment of the system in C-m
A. \[3.2 \times {10^{ - 29}}\]
B. \[3.2 \times {10^{ - 19}}\]
C. \[1.6 \times {10^{ - 29}}\]
D. \[1.6 \times {10^{ - 19}}\]

Answer 1

Hint:Before we start addressing the problem, we need to know about the electric dipole moment. It measures the separation of positive and negative electrical charges within a system, in other words, it is a measure of the system's overall polarity and its SI unit is a coulomb-meter (Cm).

Formula Used:
To find the electric dipole the formula is,
\[P = qr\]
Where, q is the charge of the dipole and r is distance between the two charges.

Complete step by step solution:
Suppose an electron and a proton are kept at a distance of \[{\rm{1}}\mathop {\rm{A}}\limits^{\rm{0}} \]. We need to find the dipole moment of the system in C-m
We know that, since the charge on an electron and a proton is equal and opposite, they will constitute an electric dipole.

The formula to find the electric dipole is given by,
\[P = qr\]
Given that, \[{\rm{r = 1}}\mathop {\rm{A}}\limits^{\rm{0}} \] and we know the charge of the electron and the proton \[q = 1.6 \times {10^{ - 19}}C\].
Then, substitute the values in above equation we get,
\[P = 1.6 \times {10^{ - 19}} \times 1 \times {10^{ - 10}}\]
\[\therefore P = 1.6 \times {10^{ - 29}}\,C - m\]
Therefore, the dipole moment of the system is \[1.6 \times {10^{ - 29}}C - m\].

Hence, option C is the correct answer.

Note: Don’t get confused with the charge of a proton and the charge of the electron. The magnitude of the charge of the proton and the charge of the electron is the same, that is, \[1.6 \times {10^{ - 19}}C\]but, the direction will be opposite to each other. The mass of the electron and proton is different that is the mass of the proton is \[1.672 \times {10^{ - 29}}kg\] and that of an electron is \[9.1 \times {10^{ - 31}}kg\].