What does the angular momentum quantum number determine in a hydrogen atom?

the kind (shape) of the orbital and the energy of the electron on the outer shell.

Explanation:

1) There are four quantum numbers:

i) Principal quantum number (n)

ii) Azimuthal quantum number (ℓ), also known as angular momentum quantum number.

iii) Magnetic quantum number (m)

iv) Spin quantum number (s)

2) The principal quantum number tells the main energy level. It can be 1, 2, 3, 4, 5, 6, 7. It is related with the orbial size. 1 is a small orbital, 7 is a big orbital.

2) The Azimuthal quantum number (ℓ) or angular momentum quantum number may be a number between 0 and n - 1.

It tells the kind of orbital, which is its shape

The correspondence is:

ℓ = 0 = s orbital,

ℓ = 1 = p orbital,

ℓ = 2 = d orbital,

ℓ = 3 = f orbital.

3) The principal quantum number (n) along with the angular momentun quantum number (ℓ), tells the energy of the electron in the hydrogen atom as per this order:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p.

You can predict that order following Aufbau rule.

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