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Which of the following is a permissable set of quantum numbers for an electron in a hydrogen atom?

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Question

Which of the following is a permissable set of quantum numbers for an electron in a hydrogen atom? The atom may be in an excited state (ie. the electron need not be in its ground state).

a) n = 6, l = -5, m_l = +4, m_s = +1/2

b) n = 4, l = -2, m_l = +2, m_s = -1/2

c) n = 2, l = 2, m_l = +1, m_s = -1/2

d) n = 5, l = 1, m_l = -1, m_s = +1/2

e) n = 3, l = 2, m_l = -2, m_s = -1

Expert Solution

Step 1

Principal Quantum Number

The principal quantum number gives the energy of an electron in a hydrogen atom. The principal quantum number actually tells us the shell or the orbit in which the electron is currently situated. The theoretical value of the principal quantum number can be from 1 to infinity. It is denoted by $n .$

Azimuthal Quantum Number

The azimuthal quantum number quantifies the position of the atomic orbital in which the electron is situated. It also tells us about the shape of the orbital where the electron is situated. An orbital can have many suborbital. The permissible number of suborbital for $n^{t h}$ orbital is from $0$ to $n - 1$ . The azimuthal quantum number is denoted by $l$ and for $n^{t h}$ orbital, it can have have $0$ to $n - 1$ quantum number.

Magnetic Quantum Number

The magnetic quantum number denoted by $m_{l}$ tells us how an orbital of quantum number $l$ is oriented in space. The magnetic quantum number $m_{l}$ can have only discrete values ranging from $- l$ to $+ l$ which one difference. That is

$m_{l} = - l, - l + 1, - l + 2, . . . ., l - 2, l - 1, l$

Spin Quantum Number

The spin quantum number tells us about the state of the spin of an electron. The electron can only occupy spin states $+ \frac{1}{2}$ and $- \frac{1}{2}$ . So the spin quantum number can only have these values. It is denoted by $m_{s}$ .

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