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How many electrons in an atom may have the following quantum numbers?

n = 4, `m_s = -1/2`

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#### Solution

Total number of electrons in an atom for a value of n = 2n^{2}

∴ For n = 4,

Total number of electrons = 2 (4)^{2}

= 32

The given element has a fully filled orbital as

1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10}.

Hence, all the electrons are paired.

∴ Number of electrons (having n = 4 and `m_s = -1/2`) = 16

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