(I) An electron and a proton are \({\bf{0}}{\bf{.53 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\;{\bf{m}}\) apart. What is their dipole moment if they are at rest?

The product of magnitude of either charge and the distance between the two charges is termed as dipole moment.

The dipole moment is given as:

\(p = Ql\)

Here, p is the dipole moment, Q is the charge and l is distance between the two equal and opposite charges.

The distance between the two charges is,\(l = 0.53 \times {10^{ - 10}}\;{\rm{m}}\).

The magnitude of charge is, \(q = 1.6 \times {10^{ - 19}}\;{\rm{C}}\)

The relation to find dipole momentis given by,

\(p = q \times l\)

Substitute the values in the above expression.

\(\begin{aligned}p &= \left( {1.6 \times {{10}^{ - 19}}\;{\rm{C}}} \right)\left( {0.53 \times {{10}^{ - 10}}\;{\rm{m}}} \right)\\p &\approx 8.5 \times {10^{ - 30}}\;{\rm{C}} \cdot {\rm{m}}\end{aligned}\)

Thus, the dipole moment is \(8.5 \times {10^{ - 30}}\;{\rm{C}} \cdot {\rm{m}}\).