Chapter 8: 80E (page 344)

A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets ${s_{T}, L_{T}}$ of their total spin and total orbital angular momentum? Ignore possibilities in which s_T is 2 or higher.

Short Answer

Expert verified

The possible combinations for s_T and l_T are $(s_{T}, l_{T}) = (0, 1), (1, 0), (1, 1), (1, 2)$

Step by step solution

definition of total orbital angular momentum

The sum of the orbital angular momenta from each electron creates the total orbital angular momentum, which has a magnitude of the square root $\sqrt{L (L + 1)} h$ where L is an integer. The range of potential values for L is determined by the orbital orientations and specific l values of each electron in the atom.

possible value for the total orbital quantum

For $s_{T} = 0$ and $j_{T} = 1$ , the possible value for the total orbital quantum number l_T allowed by the rules of addition of the angular momenta is

$l_{T} = 1$

possible values for lT

For $s_{T} = 0$ and $j_{T} = 1$ , the possible values for are

$l_{T} = 0, 1, 2$

the possible combinations for sT and lT

In total, the possible combinations for s_T and l_T are (the notation is $(s_{T}, l_{T})$

$(0, 1), (1, 0), (1, 1), (1, 2)$

$(s_{T}, l_{T}) = (0, 1), (1, 0), (1, 1), (1, 2)$

Hence the possible combinations for s_T and l_T are $(0, 1), (1, 0), (1, 1), (1, 2)$

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A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets ${s_{T}, L_{T}}$ of their total spin and total orbital angular momentum? Ignore possibilities in which s_T is 2 or higher.

Short Answer

Step by step solution

definition of total orbital angular momentum

possible value for the total orbital quantum

possible values for lT

the possible combinations for sT and lT

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A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets {sT,LT}of their total spin and total orbital angular momentum? Ignore possibilities in which sT is 2 or higher.

Short Answer

Step by step solution

definition of total orbital angular momentum

possible value for the total orbital quantum

possible values for lT

the possible combinations for sT and lT

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Modern Physics

Torque and Rotational Motion

Particle Model of Matter

Solid State Physics

Atoms and Radioactivity

Engineering Physics

Study anywhere. Anytime. Across all devices.

A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets ${s_{T}, L_{T}}$ of their total spin and total orbital angular momentum? Ignore possibilities in which s_T is 2 or higher.