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Chapter 7: Problem 85

The electron configuration of a neutral atom is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} .\) Write a complete set of quantum numbers for each of the electrons. Name the element.

Short Answer

Expert verified
The quantum numbers for each shell are as follows: \n1s electrons - (1,0,0,±1/2),\n2s electrons - (2,0,0,±1/2),\n2p electrons - (2,1,-1,±1/2), (2,1,0,±1/2), (2,1,1,±1/2) and\n3s electrons - (3,0,0,±1/2).\nThe element is Magnesium.

Step by step solution

01

Electron Configuration Interpretation

The electron configuration '1s² 2s² 2p⁶ 3s²' tells us about the distribution of electrons in the atomic shells and subshells. It means there are two electrons in the '1s' subshell, two electrons in the '2s' subshell, six electrons in the '2p' subshell, and two electrons in the '3s' subshell.
02

Quantum Numbers for 1s Electrons

For the two electrons in the '1s' subshell: \[n = 1, l = 0, m = 0\]. The spin quantum numbers will differentiate the two electrons, so one will have spin (+1/2), the other (-1/2).
03

Quantum Numbers for 2s Electrons

For the two electrons in the '2s' subshell: \[n = 2, l = 0, m = 0\]. Again, the two electrons will differ by their spin quantum numbers (one with +1/2, the other with -1/2).
04

Quantum Numbers for 2p Electrons

For the six electrons in the '2p' subshell: \[n = 2, l = 1, m = -1, 0, 1\]. With three different magnetic quantum numbers, each could accommodate two electrons, one with a +1/2 spin and the other with a -1/2 spin.
05

Quantum Numbers for 3s Electrons

For the two electrons in the '3s' subshell: \[n = 3, l = 0, m = 0\]. Once more, the two electrons differ by their spin quantum numbers.
06

Determining the Element

The total number of electrons can be found by adding up all the electrons in the configuration: 2+2+6+2 = 12. A neutral atom with 12 electrons is the element magnesium, as atomic number equals the number of electrons in a neutral atom.

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