Question

How many

(a) sub shells and

(b) electron states are in the n = 2 shell?

How many

(c) sub shells and

(d) electron states are in the n = 5 shell?

Short answer

1. There are 2 sub-shells in the n = 2 shell.
2. There are 8 electron states in the n = 2shell.
3. There are 5 sub-shells in the n = 5 shell.
4. There are 50 electron states in the n = 5 shell.

Step-by-step solution

The given data

The given n-values are:

a) n = 2

b) n = 5

Understanding the concept of the electronic configuration

A subshell is the energy level of the atom, which is defined by the number, n = 1, 2, 3.....etc.

Similarly, using this n quantum number, we can get the number of electron states using the formula. These stares define the electronic configuration of an atom.

Formula:

The number of electron states of an atom using the quantum number,

$\mathrm{Electron}\mathrm{states}=2n^2$ ……………………….(i)

a) Calculation of sub shells for n = 2

For the given quantum number, n = 2 there are 2 sub-shells in the electronic configuration.

b) Calculation of electron states for n = 2

Using the formula of equation (i), the number of electron states for can be given as:

$$\begin{gathered} \mathrm{Electrons}\mathrm{states}=2{\left(2\right)}^2 \\ =8 \end{gathered}$$

Hence, there are 8 electron states in the shell.

c) Calculation of sub shells for n = 5

For the given quantum number, n = 5 there are 5 sub-shells in the electronic configuration.

d) Calculation of electron states for n = 5

Using the formula of equation (i), the number of electron states for can be given as:

$$\begin{gathered} \mathrm{Electrons}\mathrm{states}=2{\left(5\right)}^2 \\ =50 \end{gathered}$$

Hence, there are 50 electron states in the shell.