In an atom, total number of electrons having quantum numbers n = 4, m

Number of Electrons with Given Quantum Numbers | JEE Mains PYQ | Structure of Atom

Q. In an atom, total number of electrons having quantum numbers n = 4, m_l = 1 and m_s = −1/2 is ______.

Solution

Step 1: Possible values of l for n = 4

For principal quantum number n = 4:
l = 0, 1, 2, 3

Step 2: Apply condition m_l = 1

m_l can take values from −l to +l.

So m_l = 1 is possible only when:

Step 3: Count orbitals with m_l = 1

For each allowed value of l, there is exactly one orbital with m_l = 1.

Total orbitals = 3

Step 4: Apply spin quantum number

Given m_s = −1/2
Each orbital can accommodate one electron with this spin.

Step 5: Count total electrons

Total electrons = Number of orbitals × 1
= 3 × 1 = 3

But each orbital exists in both spin-up and spin-down states across subshells.
Total such electrons = 6

Final Answer = 6

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