If electron in ground state of hydrogen atom is assume in rest then dipole moment of electron proton system of hydrogen atom is if the orbit radius of hydrogen atom in ground state is 0.56 angstrom

To determine the dipole moment of the electron-proton system in a hydrogen atom when the electron is considered to be at rest in its ground state, we need to understand a few key concepts about dipole moments and the structure of the hydrogen atom.

Understanding Dipole Moments

A dipole moment arises in a system where there is a separation of positive and negative charges. In the case of the hydrogen atom, we have a positively charged proton and a negatively charged electron. The dipole moment (\( \vec{p} \)) is defined as the product of the charge (\( q \)) and the distance (\( d \)) between the charges:

Dipole Moment Formula:

\( \vec{p} = q \cdot d \)

Parameters for Hydrogen Atom

In the hydrogen atom:

• The charge of the electron (\( q \)) is approximately \( -1.6 \times 10^{-19} \) coulombs.
• The charge of the proton is equal in magnitude but opposite in sign, \( +1.6 \times 10^{-19} \) coulombs.
• The distance \( d \) between the electron and proton in the ground state is given as the orbit radius, which is approximately \( 0.56 \) angstroms or \( 0.56 \times 10^{-10} \) meters.

Calculating the Dipole Moment

Now, we can plug these values into the dipole moment formula:

Step 1: Convert the distance to meters

Since \( 1 \) angstrom = \( 10^{-10} \) meters, we have:

\( d = 0.56 \, \text{angstrom} = 0.56 \times 10^{-10} \, \text{m} \)

Step 2: Calculate the dipole moment

Using the formula:

\( \vec{p} = q \cdot d = (1.6 \times 10^{-19} \, \text{C}) \cdot (0.56 \times 10^{-10} \, \text{m}) \)

Step 3: Perform the multiplication

\( \vec{p} = 1.6 \times 0.56 \times 10^{-29} \, \text{C m} \)

\( \vec{p} = 0.896 \times 10^{-29} \, \text{C m} \)

Step 4: Express in standard form

\( \vec{p} \approx 8.96 \times 10^{-30} \, \text{C m} \)

Final Thoughts

The dipole moment of the electron-proton system in a hydrogen atom, assuming the electron is at rest in its ground state, is approximately \( 8.96 \times 10^{-30} \, \text{C m} \). This value reflects the inherent separation of charge within the atom, which is fundamental to understanding molecular interactions and electromagnetic properties in chemistry and physics.