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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) 鈥�...(颈)

The total number of possible electron states for a given n, Nn=鈭�1n-1Nl 鈥︹赌�(颈颈)

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=卤12) can be given using equation (i) in equation (ii) with the given value n = 5 as follows:

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

Hence, the total number of electron states is 50 .

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Most popular questions from this chapter

For the situation of Problem 21, what multiple of h2/8mL2gives the energy of (a) the first excited state, (b) the second excited state, and (c) the third excited state of the system of seven electrons? (d) Construct an energy-level diagram for the lowest four energy levels of the system.

Which (if any) of the following are essential for laser action to occur between two energy levels of an atom?

(a) There are more atoms in the upper level than in the lower.

(b) The upper level is metastable.

(c) The lower level is metastable.

(d) The lower level is the ground state of the atom.

(e) The lasing medium is a gas.

An electron is in a state with n = 3. What are (a) the number of possible values of I, (b) the number of possible values of m1, (c) the number of possible values of ms, (d) the number of states in the n = 3 shell, and (e) the number of sub-shells in the n = 3shell?

For Problem 20, what multiple of h2/8mL2gives the energy of (a) the first excited state, (b) the second excited state, and (c) the third excited state of the system of seven electrons? (d) Construct an energy-level diagram for the lowest four energy levels.

How many electron states are there in the following shells: (a) n = 4 , (b) n = 1 , (c) n = 3 , (d) n = 2 ?
See all solutions

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