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Chapter 36: Problem 3

How many quantum numbers are required to specify fully the state of a hydrogen atom?

Short Answer

Expert verified
Four quantum numbers are required to fully specify the state of a hydrogen atom: the principal quantum number (\(n\)), the azimuthal quantum number (\(l\)), the magnetic quantum number (\(m_l\)), and the spin quantum number (\(m_s\)).

Step by step solution

01

Principal Quantum Number (n)

This quantum number determines the energy level or shell of an electron in an atom. It has integer values that start from 1 and increase, denoting the energy levels, commonly referred to as the k-shell, l-shell, m-shell, etc.
02

Azimuthal Quantum Number (\(l\))

This quantum number defines the shape of the orbital and can have integer values from 0 to \(n-1\). For example, if the principal quantum number (\(n\)) is 1, then \(l\) can be only 0, denoting a spherical shape.
03

Magnetic Quantum Number (\(m_l\))

This quantum number describes the orientation of the orbital in space. It can have any integral value between -l to +l including zero. If the azimuthal quantum number (\(l\)) is 2, then \(m_l\) can be -2, -1, 0, 1, or 2.
04

Spin Quantum Number (\(m_s\))

This quantum number is related to the spin of the electron which can be in two possible orientations: downward (-1/2) or upward (+1/2).

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