Question

(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?

Short answer

The dipole momentis\(8.5 \times {10^{ - 30}}\;{\rm{C}} \cdot {\rm{m}}\).

Step-by-step solution

Understanding of dipole moment

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.

Given Data

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

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

Evaluation of the dipole moment of an electron and a proton if they are at rest

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 \(8.5 \times {10^{ - 30}}\;{\rm{C}} \cdot {\rm{m}}\).