Question

How many electrons in an atom could have these sets of quantum numbers?

n=2 --> number electrons = ?

n=5, l=2 --> number electrons= ?

n=7, l=1, ml=-1 --> number electrons= ?

Answer 1

Concepts and reason

Quantum numbers describes the energy states and orbitals of the atom. Quantum numbers are classified in to four types. They are,

1.Principle quantum number

2.Angular momentum quantum number

3.Magnetic quantum number

4.Spin quantum number

Fundamentals

Principle quantum number is denoted with \(\mathrm{n}\) and it describes the energy level of the orbital. n values are started from \(1,2,3,\) so on. Calculate the number of electron in \(\mathrm{n}\) shell by using the formula \(2 \mathrm{n}^{2}\). Angular quantum number is denoted with I and its describes the shape of the orbital 

If \(\mathrm{I}=0\) then sublevel is \(\mathbf{s}\) 

If \(\mathrm{I}=1\) then sublevel is \(\mathbf{p}\) 

If \(\mathrm{I}=2\) the sublevel is \(\mathbf{d}\)

If \(\mathrm{I}=3\) the sublevel is \(\mathbf{f}\) 

Magnetic quantum number is denoted with I and it describes the orientation of the orbital in space. Number of orbitals possible for the given \(\mathrm{n}\) value is calculated by using \(\mathrm{n}^{2}\).

 

\(\mathrm{N}\) value is 2 . So, calculate the number of electron by using following formula \(2 \mathrm{n}^{2}\)

Number of electrons \(=2 \mathrm{n}^{2}\)

\(=2(2)^{2}\)

\(=8\) electrons

Thus, the number electrons present in \(\mathrm{n}=2\) shell are 8 electrons.

On substituting \(\mathrm{n}\) value in \(2 \mathrm{n}^{2}\) we get the number of electrons.

 

\(\mathrm{n}=5, l=2\)

\(l=2\) means \(\mathrm{d}\) sublevel and \(\mathrm{n}=5\) indicates 5 th energy level.

Thus, the number electrons present in \(\mathrm{n}=5\) and \(l=2\) are 10 electrons.

\(\mathrm{n}=5\) and \(l=2\) means \(5 \mathrm{~d}\) sublevel. In this level five orbitals are present. Each orbital can accommodate two electrons. So, number of electrons present in \(\mathrm{n}=5\) and \(l=2\) is 10 electrons.

 

\(\mathrm{n}=7, l=1, \mathrm{~m}_{l}=-1\)

\(l=1\) means \(\mathrm{p}\) sublevel and \(\mathrm{n}=7\) indicates 7 th energy level.

Thus, the number electrons present in \(\mathrm{n}=7, l=1,\) and \(\mathrm{m}_{l}=-1\) are 2 electrons.

\(\mathrm{n}=7, l=1,\) and \(\mathrm{m}_{l}=-1\) means \(7 \mathrm{p}\) sublevel. In this level three orbitals are present. Each orbital can accommodate two electrons. However, \(\mathrm{m}_{l}=-1\) contains 2 electrons.