Question

He quantum mechanical model of the hydrogen atom requires that if the principal quantum number = 4, there will be permitted how many orbital magnetic quantum numbers?

Answer 1

Since, Principal quantum number is 4. This means that the Electron is in Nth shell.

Now, From the Principle quantum number, the maximum possible Azimuthal or angular momentum,  Quantum number will be n. This means there will be 4 values of the azimuthal Quantum number. These will be, 0,1,2,3.

Now From this, For Each value of the Azimuthal Quantum number, value of the Magnetic Quantum number can be obtained.

For Azimuthal number 0 (s), Magnetic Quantum number (m) = 0

For Azimuthal number 1 (p), Magnetic Quantum number (m) = -1,0,1

For Azimuthal number 2 (d), Magnetic Quantum number (m) = -2,-1,0,1,2

For Azimuthal number 3 (f), Magnetic Quantum number (m) = -3,-2,-1,0,1,2,3

These are the Possible values of the Magnetic Orbital Quantum number in the case of n = 4.

Note, It is not the Filling order of the electrons because these are some sub shells which have the value of energy less than 4d or 4f.

Hope it helps.

Answer 2

Principal quantum number is 4. This means that the Electron is in Nth shell.

Now, From the Principle quantum number, the maximum possible Azimuthal or angular momentum,  Quantum number will be n. This means there will be 4 values of the azimuthal Quantum number. These will be, 0,1,2,3.

Now From this, For Each value of the Azimuthal Quantum number, value of the Magnetic Quantum number can be obtained.

For Azimuthal number 0 (s), Magnetic Quantum number (m) = 0

For Azimuthal number 1 (p), Magnetic Quantum number (m) = -1,0,1

For Azimuthal number 2 (d), Magnetic Quantum number (m) = -2,-1,0,1,2

For Azimuthal number 3 (f), Magnetic Quantum number (m) = -3,-2,-1,0,1,2,3

These are the Possible values of the Magnetic Orbital Quantum number in the case of n = 4.

Note, It is not the Filling order of the electrons because these are some sub shells which have the value of energy less than 4d or 4f.