Chapter 32: Q35P (page 969)

(a) What is the measured component of the orbital magnetic dipole moment of an electron with $m_{l} = 1 ?$ (b) What is the measured component of the orbital magnetic dipole moment of an electron with $m_{l} = - 2 ?$

Short Answer

Expert verified

(a) The orbital magnetic dipole moment of an electron with $m_{l} = 1$ is $- 9.3 \times 10^{- 24} J / T$

(b) The orbital magnetic dipole moment of an electron with $m_{l} = - 2$ is $1.9 \times 10^{- 23} J / T$

Step by step solution

Listing the given quantities

$m_{l} = 1$

$m_{l} = - 2$

Understanding the concepts of orbital angular momentum

An electron in an atom has an orbital angular momentum, and for this, we can

associate an orbital magnetic dipole moment. Orbital angular momentum is quantized. By substituting the value of $m_{l}$ , we can find the corresponding component of the orbital magnetic dipole moment.

Formula:

${μ_{o r b}}_{z} = - μ_{B} m$

(a) Calculations of the orbital magnetic dipole moment of an electron with ml=1

${μ_{o r b}}_{z} = - μ_{B} m_{l}$

For $m_{l} = 1$

role="math" localid="1663153694077" $\begin{array}{rcl} {μ_{o r b}}_{z} & = & - μ_{B} m_{l} \\ = & - μ_{B} \\ = & - 9.3 \times 10^{- 24} J / T \end{array}$

The orbital magnetic dipole moment of an electron with $m_{l} = 1$ is $- 9.3 \times 10^{- 24} J / T$

(b) Calculations of theorbital magnetic dipole moment of an electron with ml=-2

${μ_{o r b}}_{z} = - μ_{B} m_{l}$

For $m_{l} = - 2$

$\begin{array}{rcl} {μ_{o r b}}_{z} & = & - μ_{B} m_{l} \\ = & + 2 μ_{B} \\ = & 2 \times 9.27 \times 10^{- 24} J / T \\ = & 1.9 \times 10^{- 23} J/T \end{array}$

The orbital magnetic dipole moment of an electron with $m_{l} = - 2$ is $1.9 \times 10^{- 23} J / T$

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(a) What is the measured component of the orbital magnetic dipole moment of an electron with $m_{l} = 1 ?$ (b) What is the measured component of the orbital magnetic dipole moment of an electron with $m_{l} = - 2 ?$

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of orbital angular momentum

(a) Calculations of the orbital magnetic dipole moment of an electron with ml=1

(b) Calculations of theorbital magnetic dipole moment of an electron with ml=-2

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(a) What is the measured component of the orbital magnetic dipole moment of an electron withml=1?(b) What is the measured component of the orbital magnetic dipole moment of an electron withml=-2?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of orbital angular momentum

(a) Calculations of the orbital magnetic dipole moment of an electron with ml=1

(b) Calculations of theorbital magnetic dipole moment of an electron with ml=-2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Electricity and Magnetism

Force

Engineering Physics

Energy Physics

Electric Charge Field and Potential

Study anywhere. Anytime. Across all devices.

(a) What is the measured component of the orbital magnetic dipole moment of an electron with $m_{l} = 1 ?$ (b) What is the measured component of the orbital magnetic dipole moment of an electron with $m_{l} = - 2 ?$