Question

How many electrons in an atom can share the quantum numbers n = 2, l = 1?

1
3
6
10

Answer 1

Answer : The number of electrons held in n = 2, l = 1 are, 6 electrons

Explanation :

There are 4 quantum numbers :

Principle Quantum Numbers : It describes the size of the orbital. It is represented by n. n = 1,2,3,4....

Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...

Magnetic Quantum Number : It describes the orientation of the orbitals. It is represented as
`m_l`. The value of this quantum number ranges from
`(-l\text{ to }+l)`. When l = 2, the value of
`m_l` will be -2, -1, 0, +1, +2.

Spin Quantum number : It describes the direction of electron spin. This is represented as
`m_s` The value of this is
`+(1)/(2)` for upward spin and
`-(1)/(2)` for downward spin.

As we are given that,

`n=2`

`l=1`

`m_l=-1,0,1`

`m_s=+(1)/(2)\text{ and }-(1)/(2)` (For each sub-shell)

From this we conclude that, there are 3 orbitals and each orbital contains 2 electrons. So, the number of electrons held in an atom are,
`3* 2=6` electrons.

Hence, the number of electrons held in n = 2, l = 1 are, 6 electrons

Answer 2

principal quantum number is n = 2, principal quantum number gives the energy shells electrons reside in,
angular momentum quantum number , these are the number of subshells and gives how many subshells are there in energy shells, values for l range from 0 to n-1
magnetic quantum number -m- gives the specific orbital in the subshells and their orientation.
spin quantum number gives the spin of the electrons.

in this case, n = 2
the types of subshells in n=2 are 0 and 1
0 - s subshell
1 - p subshell
the specific number of orbitals are given by -l to +l
when l = 1
then -1, 0 and +1
therefore there are 3 orbitals in p subshell and orbitals are in 3 orientations
each orbital can hold a maximum of 2 electrons,
since there are 3 orbitals each holding 6, there are 6 electrons to which these quantum numbers are the same
answer is 6