Question

Which one contains up to ten electrons from the following?
A.$1s$
B.$2s$
C.$3s$
D.$3p$
E.$3d$

Answer 1

To answer this question, you must recall the quantum numbers. Using the value of the azimuthal quantum number, we can determine the number of possible orbitals and hence the number of electrons.

Formula Used:
${\text{number of subshells = }}2l + 1$
Where l is the orbital number ( s = 0, p = 1, d = 2 and f = 3)

Complete step by step solution:
Quantum numbers describe the position, space orientation, energy and possible interaction of electrons completely in an atom. An orbital is basically designated by three quantum numbers, $n:$ Principal quantum number, $l:$Azimuthal quantum number and ${m_l}:$Magnetic quantum number.
The number of electrons present in each subshell is 2.
For $1s$ orbital, $l = 0$ , thus the number of orbitals $= {m_l} = 1$ and the number of electrons is 2
For $2s$ orbital, $l = 0$ , thus the number of orbitals $= {m_l} = 1$ and the number of electrons is 2
For $2p$ orbital, $l = 1$, thus the number of orbitals $= {m_l} = 2(1) + 1 = 3$ and the number of electrons is 6
For $3s$ orbital, $l = 0$ , thus the number of orbitals $= {m_l} = 1$ and the number of electrons is 2
For $3p$ orbital, $l = 1$, thus the number of orbitals $= {m_l} = 2(1) + 1 = 3$ and the number of electrons is 6
For $3d$ orbital, $l = 2$, thus the number of orbitals $= {m_l} = 2(2) + 1 = 5$ and the number of electrons is 10.
Hence, only 3d orbital has a total of 10 electrons.

So, the correct option is E.

Note:
The principal quantum number $\left( n \right)$ is a positive integer. It determines the size and energy of the orbitals. We know that the size of energy shells increases with increasing $n$. Thus we can say that the orbital size also increases with $n$.
Azimuthal quantum number $\left( l \right)$ is an integer having all values between $0$ and $n - 1$. It is known as a subsidiary quantum number and is used to represent a subshell. The azimuthal quantum number is also used to define the shape of an orbital.
Magnetic quantum number $\left( {{m_l}} \right)$ is an integer having values between $- l$ to $+ l$ including zero. It gives information about the orientation of an orbital with respect to the coordinate axis.