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How many possible states are there for the l = 4 state?

Question

How many possible states are there for the l = 4 state?

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Solution

The quantum number l is known as the azimuthal quantum number or the orbital quantum number. It defines the shape of the electron's orbital and contributes to the electron's energy and angular momentum.

The possible states for a given l value can be determined by the magnetic quantum number m_l. The magnetic quantum number m_l can have values ranging from -l to +l, including zero.

So, for l = 4, the possible m_l values are -4, -3, -2, -1, 0, 1, 2, 3, 4.

Therefore, there are 9 possible states for the l = 4 state.

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