Chapter 7: Q38E (page 281)

A particle orbiting due to an attractive central force has angular momentum $L = 1.00 \times 10^{- 33} kg . m / s$ What z-components of angular momentum is it possible to detect?

Short Answer

Expert verified

The possible z-components of angular momentum are,

$L_{z} + 0, \pm h, \pm 2 h, \pm 3 h, \pm 4 h, \pm 5 h, \pm 6 h . \pm 7 h, \pm 8 h, \pm 9 h$

Step by step solution

A concept:

The azimuthal quantum number specifies the shape and angular momentum of the orbital in space.

Getting the value of I :

Consider the given data as below.

Angular momentum, $L = 1.00 \times 10^{- 33} kg . m / s$

The angular momentum is given by,

$L = \sqrt{I (I + 1)} \times h$ ….. (1)

Where, I is the Azimuthal Quantum number, h is Plank’s constant that is $1.055 \times 10^{- 34} J . s .$

$9.478 = \sqrt{I (I + 1)} I^{2} + I - 89.832 = 0$

Solving above equation gives you get,

I = 9

z-components of angular momentum:

As you know that, z-component to angular momentum,

$L_{z} = m_{l} h$

Where, $m_{l}$ is the magnetic quantum number that is $0, \pm 1, \pm 2, . . . \pm I$

Hence, possible z-components are,

$L_{z} + 0, \pm h, \pm 2 h, \pm 3 h, \pm 4 h, \pm 5 h, \pm 6 h . \pm 7 h, \pm 8 h, \pm 9 h$

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A particle orbiting due to an attractive central force has angular momentum $L = 1.00 \times 10^{- 33} kg . m / s$ What z-components of angular momentum is it possible to detect?

Short Answer

Step by step solution

A concept:

Getting the value of I :

z-components of angular momentum:

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A particle orbiting due to an attractive central force has angular momentum L=1.00×10-33kg.m/s What z-components of angular momentum is it possible to detect?

Short Answer

Step by step solution

A concept:

Getting the value of I :

z-components of angular momentum:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Further Mechanics and Thermal Physics

Work Energy and Power

Modern Physics

Mechanics and Materials

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

A particle orbiting due to an attractive central force has angular momentum $L = 1.00 \times 10^{- 33} kg . m / s$ What z-components of angular momentum is it possible to detect?