   Chapter 30, Problem 47PE

Chapter
Section
Textbook Problem

(a) List all possible sets of quantum numbers ( n , l , m l , m s ) for the n = 3 shell, and determine the number of electrons that can be in the shell and each of its subshells.(b) Show that the number of electrons in the shell equals 2n2and that the number in each subshell is 2 ( 2 l + 1 ) .

To determine

(a)

All the possible sets of quantum numbers(n,l,ml,ms)for then=3shell and the number of electrons that can be in the shell and each of its subshells.

Explanation

Formula used:

The number of electron present in shells is calculated by the formula,

Number of electrons=2n2       ...... (1)

The number of electrons in each subshell is given by the formula,

Number of electrons=2(2l+1)       ...... (2)

Calculation:

The value oflcan be calculated as,

l=(n1)to0l=2,1,0

The valuel=0corresponds to3ssubshell,l=1corresponds to3psubshell andl=2corresponds to3dsubshell.

The possible quantum numbers(n,l,ml,ms)for3sare given below.

nlmlms300±12}=2electrons

The possible quantum numbers(n,l,ml,ms)for3pare given below.

nlmlms311±12310±12311±12}=6electrons

The possible quantum numbers(n,l,ml,ms)for3dare given below

To determine

(b)

The number of electrons in shell equals2n2and the number of electrons in each subshell is2(2l+1).

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