# Orbital quantum number in the shell model

• burgjeff
In summary: Therefore, the Orbital angular momentum quantum number is not restricted by the principal quantum number in the nuclear shell model.In summary, the Orbital angular momentum quantum number is not restricted by the principal quantum number in the nuclear shell model, unlike in the atomic shell model. Additionally, the principal quantum number does not correspond to energy in the nuclear shell model.
burgjeff
Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?

Last edited:
burgjeff said:
Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model?
Who says it isn't?
Also, does the principal quantum number even correspond to energy in the shell model?
No it doesn't. Neither does it correspond to energy in the atomic shell model.

burgjeff said:
Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?
burgjeff, Atomic states correspond to energy levels in a Coulomb potential, the energy E ~ 1/n2, where n is the principal quantum number.

In the nuclear single particle shell model, the states are levels in a central potential which is not Coulomb. Although a similar spectroscopic notation is used to denote these levels, such as 2p or 1d, the first number is not a principal quantum number, it's just a serial number. That is, 1d simply denotes the lowest level with ℓ = 2.

## 1. What is the orbital quantum number in the shell model?

The orbital quantum number, denoted by the letter l, is a quantum number that describes the shape of an electron's orbital in an atom. It determines the subshell in which the electron is located, and it can have values ranging from 0 to n-1, where n is the principal quantum number.

## 2. How does the orbital quantum number affect the energy of an electron?

The higher the orbital quantum number, the higher the energy of the electron. This is because electrons with higher values of l are found farther away from the nucleus and experience less attraction, resulting in higher energy levels.

## 3. How many possible values can the orbital quantum number have?

There are n possible values for the orbital quantum number, where n is the principal quantum number. For example, if n = 3, the possible values for l would be 0, 1, and 2.

## 4. What is the relationship between the orbital quantum number and the angular momentum of an electron?

The orbital quantum number is related to the angular momentum of an electron by the equation L = √(l(l+1)ħ, where ħ is the reduced Planck's constant. This means that the higher the orbital quantum number, the greater the angular momentum of the electron.

## 5. How does the orbital quantum number affect the number of electrons in a subshell?

The orbital quantum number determines the number of orbitals in a subshell. The number of orbitals in a subshell is equal to 2l+1. For example, a subshell with l=2 would have 2(2)+1 = 5 orbitals, which can hold a maximum of 10 electrons (2 electrons per orbital).

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