If an electron is in the state characterized by the quantum numbers n=4, l=2, wh

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Question: If an electron is in the state characterized by the quantum numbers n=4, l=2, what is the value of m_l?

Options:

Correct Answer: All of the above

Solution:

For l=2, m_l can take values -2, -1, 0, 1, 2. Therefore, all of the options are valid.

If an electron is in the state characterized by the quantum numbers n=4, l=2, what is the value of m_l?

If an electron is in the state characterized by the quantum numbers n=4, l=2, what is the value of m_l?

Step 1: Understand the quantum numbers. The quantum number 'n' represents the energy level, and 'l' represents the angular momentum quantum number.
Step 2: Identify the value of 'l'. In this case, 'l' is given as 2.
Step 3: Determine the possible values of 'm_l'. The magnetic quantum number 'm_l' can take values from -l to +l, including zero.
Step 4: Calculate the range of 'm_l' values. Since 'l' is 2, 'm_l' can be -2, -1, 0, 1, or 2.
Step 5: Conclude that all these values (-2, -1, 0, 1, 2) are valid for 'm_l'.

Quantum Numbers – Quantum numbers describe the properties of atomic orbitals and the electrons in those orbitals. The principal quantum number (n) indicates the energy level, the azimuthal quantum number (l) indicates the subshell, and the magnetic quantum number (m_l) indicates the orientation of the orbital.
Magnetic Quantum Number (m_l) – The magnetic quantum number (m_l) can take integer values ranging from -l to +l, including zero. This means for a given l, there are (2l + 1) possible values for m_l.