Quantum numbers arise naturally from the mathematics used to describe the possib

Question

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply n = 5, l = 4, m 0, m_l = 0, m_s = +1/2 n = 3, l = -1, m_l = 0, m_s = +1/2 n = 3, l = 1, m_l = 0, m_s = +1/2 n = 4, l = 2, m_l = 3, m_s = -1/2 n = 2, l = 2, m_l = -1, m_s = +1/2 n = 2, l = 1, m_l = 0, m_s = -1

Explanation / Answer

Rules

The highest value for azimuthal quantum number l is n-1

m can have values -l to +l through zero.

s canhave only two values +1/2 and -1/2.

Now the allowable combinations are

n=5, l= 4, m =0 and s= 1/2

Second one is forbidden as l value can not be negative.

third one n=3, l= 1, m= 0 and s = +1/2 is allowed.

fourth one is not allowed as m can not have larger value than l

fifth is also not allowed as l can not have same value as n.

last one is not allowed as s value can not be -1.

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