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Question

Give the atomic number of the inert gas in which the total number of d electrons is equal to the difference between the total number of p and s electrons.

Solution
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Hint: The elements belong to group $$18$$ of the periodic table are called inert gas elements.

Step 1: Inert Gas Elements and their atomic numbers.
General electronic configuration is $$ns^2$$ $$np^6$$
Helium ($$He$$) is 2. Electronic configuration is $$1s^2$$
Neon ($$Ne$$) is 10. Electronic configuration is $$1s^2 2s^2 2p^6 $$.
Argon ($$Ar$$) is 18. Electronic configuration is $$1s^2 2s^2 2p^6 3s^2 3p^6$$
Krypton($$Kr$$) is36. Electronic configuration is $$1s^2 2s^2 2p^6 3s^2 3p^6 $$ $$3d^{10} 4s^2 4p^6$$
Xenon ($$Xe$$) is 54. Electronic configuration is $$1s^{2} 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6 $$
Radon ($$Rn$$) is 86. Electronic Configuration is $$ 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^10 6s^2 6p^6 $$

Step 2: Number of d electrons.
$$He$$: We see that there are no $$d$$ electrons in it.
$$Ne$$: There are no $$d$$ electrons. The number of $$s$$ electrons is 4 and the number of $$p$$ electrons is 6.
The difference is $$6 - 4 = 2$$ which is not equal to the number of $$d$$ electrons present.
$$Ar$$: There are no $$d$$ electrons. The number of $$s$$ electrons is 6 and the number of $$p$$ electron is 12.
The difference is $$12-6=6$$ which is not equal to the number of $$d$$ electrons present.
$$Kr$$: The number of $$d$$ electrons = 10
The number of $$s$$ electrons = 8
The number of $$p$$ electrons = 18
The difference between the number of $$s$$ and the number of $$p$$ electrons is $$18-8=10$$ which is equal to the number of $$d$$ electrons present.
Therefore in krypton ($$Kr$$) ( atomic number 36 ), total number of $$d$$ electrons is equal to the difference between the total number of $$p$$ and $$s$$ electrons.

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