What is the difference between shell, subshell, and orbital?

Answer 1

The electron's wave function forms standing waves, known as stationary states, which are defined by three quantum numbers, according to the Schroedinger equation for an electron bound to a spherically symmetric coulomb potential of a hydrogen-like nuclei.

Principal Quantum Number (#n#) : #n=1,2,3, \cdots \infty# For single electron systems the allowed energy values (energy levels) are determined purely by the principle quantum number. This quantum number can only take integer values starting with #1# with no upper bound. All the electronic states with the same principle quantum number are said to belong to the same shell. The #n=1# states are labeled K-shell , #n=2# states are labeled L-shell , #n=3# states are labeled M-shell , #n=4# states are labeled N-shell and so on.
Angular Momentum Quantum Number (#l#): #l=0,1,2, ..., n-1#. This quantum number determines the magnitude of the orbital angular momentum of the electron. It can take only integer values starting from 0 but has an upper bound. It can only go up to a number that is one less than the principal quantum number. While the shells are a bigger group of quantum states, this quantum number breaks them into smaller groups of quantum states called sub-shells. All quantum states with the same orbital angular momentum quantum number are said to belong to the same sub-shell. The #l=0# states are labeled s-subshell, #l=1# states are labeled p-subshell, #l=2# states are labeled d-subshell, #l=3# states are labeled f-subshell and so on. Thus the quantum states belonging to a shell with principal quantum number #n# are divided into #n# subshells.
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Answer 2

An orbital is a region of space around the nucleus that is described by a set of quantum numbers. A shell is a group of atomic orbitals with the same principal quantum number (n). A subshell is a group of atomic orbitals within a shell with the same azimuthal quantum number (l).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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