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(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

Expert verified

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

Step by step solution

01

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.

02

Given Data

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

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

03

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

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Most popular questions from this chapter

(III) In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius \({\bf{0}}{\bf{.53 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\;{\bf{m}}\). (a) What is the electric potential at the electron’s orbit due to the proton? (b) What is the kinetic energy of the electron? (c) What is the total energy of the electron in its orbit? (d) What is the ionization energy— that is, the energy required to remove the electron from the atom and take it to \({\bf{r = }}\infty \), at rest? Express the results of parts (b), (c), and (d) in joules and eV.

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