Concept explainers
(a)
The energy supplied to reverse the direction of a magnetic dipole moment due to the spin of an electron.
(a)
Answer to Problem 18E
The energy required to reverse the direction of the magnetic dipole moment of an electron due to its spin is
Explanation of Solution
A loop wire carrying a current in a magnetic field is called a magnetic dipole.
Write the expression to find the potential energy of a magnetic dipole.
Here,
The
Here,
Conclusion:
Substitute
Substitute
Here,
Substitute
Here,
The energy required to reverse the dipole moment due to the spin of an electron will be the difference between the energies when the dipole moments are parallel and anti-parallel to the field.
Thus, energy required to reverse the direction of the magnetic dipole moment is,
Here,
Substitute
Therefore, the energy required to reverse the direction of the magnetic dipole moment of an electron due to its spin is
(b)
The ratio of energy required to reverse the direction of the magnetic dipole moment of an electron due to spin to the energy needed to remove an atom from a normal hydrogen atom.
(b)
Answer to Problem 18E
The ratio of energy required to reverse the direction of the magnetic dipole moment of an electron due to spin to the energy needed to remove an atom from a normal hydrogen atom is
Explanation of Solution
The energy needed to remove an atom from a normal hydrogen atom is,
Here,
From part (a) the value of
Conclusion:
The ratio of energy required to reverse the direction of the magnetic dipole moment of an electron due to spin to the energy needed to remove an atom from a normal hydrogen atom is,
Therefore, the ratio of energy required to reverse the direction of the magnetic dipole moment of an electron due to spin to the energy needed to remove an atom from a normal hydrogen atom is
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Chapter 19 Solutions
General Physics, 2nd Edition
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