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If $l = 3$, then type and number of orbital is:
A) 3p, 3
B) 4f, 14
C) 5f, 7
D) 3d, 5


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Last updated date: 13th Jun 2024
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Answer
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Hint: To answer this question, you should have the knowledge of quantum numbers and orbitals. $l$ is known as the azimuthal quantum number. Values of $l$ range from 0 to $n - 1$ and for each value of $l$, there is a corresponding subshell assigned.

Complete step by step solution:
Atomic orbitals are precisely distinguished by quantum numbers. Each orbital is designated by three quantum numbers and these are: $n$, $l$ and $m$.
You should have knowledge of $n$, $l$ quantum numbers for this question. So let us discuss them one by one.
- $n$ is known as the principal quantum number and it is a positive integer with value = 1, 2, 3...... . This quantum number identifies the shell.
- $l$ is known as the azimuthal quantum number or orbital quantum number. For, a given value of n, $l$ can have values from 0 to $n - 1$. For example, when n=3, the possible values for $l$= 0, 1, 2. For each value of $l$, there is a corresponding sub-shell and subshells are represented as follows:


Value of $l$Subshell notation
0$s$
1$p$
2$d$
3$f$
4...$g$...


Thus, values of $l$ define the sub-shells.
There are $(2l + 1)$ orbitals in each subshell. For example, when $l$= 2, orbitals are five $(2 \times 2 + 1 = 5)$
Now, we are given in that $l$= 3,
Therefore, for $l$= 3, subshell is $f$.
Orbitals for $l$= 3: $2l + 1 = 2 \times 3 + 1 = 7$ orbitals.

Hence, according to the above calculation, the correct option is C.

Note: In an orbital, maximum two electrons can exist and each electron has an opposite spin. We have calculated that, for $l$= 3, subshell is $f$ and there are 7 orbitals. So, the maximum number of electrons that can exist in $f$ subshell are 14.