The speed and radial acceleration for a ground-state electron in the hydrogen atom.
Answer to Problem 16P
The speed for a ground-state electron in the hydrogen atom is
Explanation of Solution
If an electron rotates around the nucleus then the expression for speed is given below:
Here,
Multiply by
Value of
Write the expression for radial acceleration.
Here,
For hydrogen like lithion ion
Write the expression for maximum Coulomb force.
Here,
Write the expression for centripetal force.
Here,
From equation (III) and (IV) solve and rearrange the equation for value of
Write the expression for radius.
Here,
Substitute
Conclusion:
Substitute
Substitute
For Lithium ion:
Substitute
Substitute
Thus, the speed for a ground-state electron in the hydrogen atom is
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Chapter 4 Solutions
Modern Physics for Scientists and Engineers
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