Question

The following sets of quantum numbers, listed in the order n, l, m_l, and m_s were written for the last electrons added to an atom. Identify which sets are valid and classify the others by the rule or principle that is violated. Drag each item to the appropriate bin.

Quantum Number order: n, l, m_l, m_s

Answer 1

 

Concept and reason

The concept used is to identify the valid set of quantum numbers for the last electrons added to an atom.

Fundamentals

The four quantum numbers required to describe an atom are principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number. Principal quantum number: It describes the energy level of an electron. It is denoted by n. The value of \(\mathrm{n}\) ranges from 1 to the level of the electron in the outermost orbit. Azimuthal quantum number: It describes the sub-shell of an electron. I denote it.

The value of I ranges from 0 to \((n-1)\)

Magnetic quantum number: It describes the energy levels of the sub-shell of an electron. It is denoted by \(m_{l}\).

The value of \({ }^{m_{l}}\) ranges from \(-l\) to \(+l\).

Spin quantum number: It describes the spin of an electron. It is denoted by \(m_{s}\). The value of \({m_{s}}\) can either be \(+1 / 2\) or \(-1 / 2\) According to Pauli's exclusion principle, no two electrons can have same four quantum numbers.

 

Consider the set as follows:

\(\begin{array}{lll}5 & 0 & 0 & +1 / 2\end{array}\)

\(\begin{array}{llll}5 & 0 & 0 & -1 / 2\end{array}\)

It is a valid set.

Explanation

Here, the value of \(n\) is \(5 .\) So, \(l\) can be 0,1,2,3,4 .

Here, \(l=1 .\) So, \(m_{l}\) can be -1,0,+1

Here, \(m_{l}=0 .\) So, \(m_{s}\) can be \(+1 / 2,-1 / 2\) There is no repetition of the quantum numbers. [Hint for the next step] Identify whether the given set is valid or not.

 

Consider the set as follows:

\(\begin{array}{lll}4 & 1 & -1 & +1 / 2\end{array}\)

\(\begin{array}{lll}4 & 1 & 0 & +1 / 2\end{array}\)

\(41+1+1 / 2\)

It is a valid set.

Explanation

Here, the value of \(n\) is \(4 .\) So, \(l\) can be 0,1,2,3 .

Here, \(l=1 .\) So, \(m_{l}\) can be -1,0,+1

 

Here, \(m_{l}=-1,0,+1 .\) So, \(m_{s}\) can be \(+1 / 2,-1 / 2\) There is no repetition of the quantum numbers. [Hint for the next step] Identify whether the given set is valid or not.

 

Consider the set as follows:

\(\begin{array}{lll}3 & 2 & -1 & +1 / 2\end{array}\)

\(320+1 / 2\)

\(32+1+1 / 2\)

\(320+1 / 2\)

\(32+2+1 / 2\)

It is not a valid set. There is a violation of Pauli exclusion principle.

Explanation

Here, the value of \(n\) is \(3 .\) So, \(l\) can be 0,1,2 .

Here, \(l=2 .\) So, \(m_{l}\) can be -2,-1,0,+1,+2

Here, \(m_{l}=-2,-1,0,+1,+2 .\) So, \(m_{s}\) can be \(+1 / 2,-1 / 2\) There is repetition of the quantum numbers.

\(320+1 / 2\) is repeated twice. [Hint for the next step] Identify whether the given set is valid or not.

 

Consider the set as follows:

\(\begin{array}{lll}3 & 1 & -1 & +1 / 2\end{array}\)

\(\begin{array}{lll}3 & 1 & 0 & +1 / 2\end{array}\)

\(33+1+1 / 2\)

It is not a valid set. There are other violations.

 

The valid and non-valid sets of quantum numbers are as follows:

Here, the value of \(n\) is \(3 .\) So, \(l\) can be 0,1,2 .

Here, \(l=1 .\) So, \(m_{l}\) can be \(-1,0,+1 . \mid\) cannot be 3 .

Here, \(m_{l}=-1,0,+1 .\) So, \(m_{s}\) can be \(+1 / 2,-1 / 2\).

There is a value of \(l=3\) that is not possible for the given quantum number, \(n=3\).