Question 52

The number of electrons present in all the completely filled subshells having $$n = 4$$ and $$s = +\frac{1}{2}$$ is ______ (Where $$n$$ = principal quantum number and $$s$$ = spin quantum number)


Correct Answer: 16

For $$n = 4$$, the possible subshells are: $$4s, 4p, 4d, 4f$$.

The completely filled subshells for $$n = 4$$ are:

- $$4s$$: 2 electrons (completely filled)

- $$4p$$: 6 electrons (completely filled)

- $$4d$$: 10 electrons (completely filled)

- $$4f$$: 14 electrons (completely filled)

Total electrons in all completely filled subshells with $$n = 4$$: $$2 + 6 + 10 + 14 = 32$$

Now, electrons with $$s = +\frac{1}{2}$$: In each completely filled subshell, exactly half the electrons have $$s = +\frac{1}{2}$$ and the other half have $$s = -\frac{1}{2}$$.

Number of electrons with $$s = +\frac{1}{2}$$: $$\frac{32}{2} = 16$$

The answer is $$\boxed{16}$$.

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