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Chapter 40: Q2P (page 1247)

How many electron states are there in a shell defined by the quantum number n = 5 ?

Short Answer

Expert verified

There are 50 electron states in the shell defined by the quantum number n = 5 .

Step by step solution

01

The given data

The given quantum number, n = 5

02

Understanding the concept of electron states in a shell

Using the concept of possible electron states for a given quantum number, we can get the required value of the number of the electron states in a shell.

Formulae:

The number of possible electron states for each value of lis, Nl=2(2l+1) …...(i)

The total number of possible electron states for a given n, Nn=∑1n-1Nl ……(ii)

03

Calculation of the number of electron states in a shell

We know that for a given quantum number n, there are n possible values of l, ranging from 0 to (n-1) .

Thus, the total number of electron states ( ms=±12) can be given using equation (i) in equation (ii) with the given value n = 5 as follows:

Nn=∑1n-122l+1=2∑1n-12l+1=2n2=2(5)2 =50

Hence, the total number of electron states is 50 .

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