Question

For ‘l’, the minimum value is _____ and the maximum value is _______.
A.1, n
B.0, \[{\text{n - 1}}\]
C.1, \[{\text{n - 1}}\]
D.0, n

Answer 1

Hint: Quantum numbers are the index numbers which are used to specify the position and energy of an electron in an atom. There are four quantum numbers. The letter ‘l’ is used to designate the azimuthal or orbital or angular quantum number. The value of ‘l’ depends on the value of the quantum number ‘n’, which is the principal quantum number.

Complete step by step answer:
The individual spectral lines of the hydrogen spectrum were found to consist of a group of closely spaced lines. Such a spectrum is called a fine structure. The fine structure of a spectral line is explained by assuming that all electrons of a shell do not have the same energy and each shell is composed of a number of subshells. These are specified by a secondary quantum number which is designated by ‘l’. For a given value of the principal quantum number ‘n’, ‘l’ can have values from zero to \[{\text{n - 1}}\] .
Each value of ‘l’ represents different subshells which are designated as s, p, d, f etc. For example, for n is equal to 1, l is equal to 0. It means the first shell has only one subshell which is designated by ‘s’ or ’1s’ where 1 represents the number of shells and s represents the subshell.Similarly, for n equals to 2, ${\text{l = 0}}$ to \[{\text{n - 1}}\] , which equals to 0 to \[{\text{2 - 1}}\] , i.e. l equals to 0,1. Thus, the second shell has two subshells 2s and 2p.
For n equals to 3, ${\text{l = 0}}$ to \[{\text{n - 1}}\] , which equals to 0 to \[{\text{3 - 1}}\] , i.e. l equals to 0,1,2. Thus, the second shell has three subshells 3s, 3p and 3d.

Value of l	0	1	2	3
Designation	s	p	D	f

Hence, for ‘l’, the minimum value is 0 and the maximum value is \[{\text{n - 1}}\] .

So, the correct option is B.

Note:
The l values give the energy of the electron due to angular momentum of the electron. The angular momentum of the electron is given by:
Angular momentum $ = \sqrt {{\text{l}}\left( {{\text{l + 1}}} \right)} \dfrac{{\text{h}}}{{{{2\pi }}}}$
The l values also help to calculate the total number of electrons in a given subshell. The total number of electrons in a given subshell with a given l value is equal to ${\text{2}}\left( {{\text{2l + 1}}} \right)$ .