Which of the following spectroscopic notations are not allowed?

\[\begin{array}{l}{\rm{(a)5}}{{\rm{s}}^{\rm{1}}}\\{\rm{(b)1}}{{\rm{d}}^{\rm{1}}}\\{\rm{(c)4}}{{\rm{s}}^{\rm{3}}}\\{\rm{(d)3}}{{\rm{p}}^{\rm{7}}}\\{\rm{(e)5}}{{\rm{g}}^{{\rm{15}}}}{\rm{.}}\end{array}\]

State which rule is violated for each that is not allowed

The method to analyse the quality and the characteristics of the material by emitting the radiations is called spectroscopy.

1. Given spectroscopic notation\[5{s^1}\]
2. Given spectroscopic notation\[1{d^1}\]

c)Given spectroscopic notation\[4{s^3}\]

d)Given spectroscopic notation\[3{p^7}\]

e)Given spectroscopic notation\[5{g^{15}}\]

Formula used: Two or more identical particles cannot occupy the same quantum state at the same time, according to the Pauli Exclusive principle. Same quantum state cannot be shared by the two or more particles with the same identity.

a)

Given spectroscopic notation\[5{s^1}\]

Here, we have\[l < n\].

Also, Number of electrons in sub-shell is\[ \le 2\left( {2l + 1} \right)\]

For sub-shell s, l=0

Maximum number of electrons in s subshell

\[\begin{array}{l}s = 2\left( {2\left( 0 \right) + 1} \right)\\s = 2\end{array}\]

Thus,\[5{s^1}\]allowed.

Hence, the spectroscopic notation is\[5{s^1}\]allowed.

q

b)

Given spectroscopic notation\[1{d^1}\]

Here, we have\[l < n\]

Thus,\[1{d^1}\]is not allowed.

Hence,\[1{d^1}\] the spectroscopic notation is not allowed.

c)

Given spectroscopic notation\[4{s^3}\]

Here, we have\[l < n\]

Also, Number of electrons in sub-shell is\[ \le 2\left( {2l + 1} \right)\]

For sub-shell s, l=1

Maximum number of electrons in s subshell

\[\begin{array}{l}s = 2\left( {2\left( 1 \right) + 1} \right)\\s = 6\end{array}\]

Thus,\[4{s^3}\]is not allowedbecause only two electrons are allowed in s subshell.

Hence, the spectroscopic notation is \[4{s^3}\]is not allowed.

d)

Given spectroscopic notation\[3{p^7}\]

Here, we have\[l < n\]

Also, Number of electrons in sub-shell is\[ \le 2(2l + 1)\]

For sub-shell s, l=1

Maximum number of electrons in s subshell

\[\begin{array}{l}s = 2\left( {2\left( 1 \right) + 1} \right)\\s = 6\end{array}\]

Thus,\[3{p^7}\]is not allowedbecause only two electrons are allowed in s subshell.

Hence, the spectroscopic notation is \[3{p^7}\]is not allowed.

e)

Given spectroscopic notation\[5{g^{15}}\]

Here, we have\[l < n\]

Also, Number of electrons in sub-shell is\[ \le 2(2l + 1)\]

For sub-shell s, l=4

Maximum number of electrons in s subshell

\[\begin{array}{l}s = 2\left( {2\left( 4 \right) + 1} \right)\\s = 18\end{array}\]

Thus,\[5{g^{15}}\]is not allowedbecause only two electrons are allowed in s subshell.

Hence, the spectroscopic notation is\[5{g^{15}}\]is not allowed.