Question

The set of quantum numbers not applicable to an electron is given by:
$(i){\text{ 1, 1, 1, + }}\dfrac{1}{2}$
$(ii){\text{ 1, 0, 0, + }}\dfrac{1}{2}$
$(iii){\text{ 1, 0, 0, - }}\dfrac{1}{2}$
$(iv){\text{ 2, 0, 0, + }}\dfrac{1}{2}$

Answer 1

We will check the values of principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number for an electron. We will check each set of quantum numbers which are given in the options and will judge which set of quantum numbers is not applicable for an electron.

Complete answer:
Principal Quantum refers to the shell in which an electron is currently available. Therefore we know that the value of principal quantum can vary from one to ${n^{th}}$ shell. It is represented by $n$ . Then we have an azimuthal quantum number which is represented as $l$ . The value of azimuthal quantum for a particular value of principal quantum number can vary from $0$ to $n + 1$ . Then we have a magnetic number which is represented as $m$ whose value can vary from $- l$ to $+ l$ for a given azimuthal quantum number. Then we have a spin quantum number which is represented as ${m_s}$ whose value is always equal to $+ \dfrac{1}{2}$ or $- \dfrac{1}{2}$ .
Therefore we can summarize that,
$n{\text{ = 1,2,3}}..........$
$l{\text{ = 0 to n - 1 = 0,1,2,3}}.........$
$m{\text{ = }} - l{\text{ }}to{\text{ }} + l$
${m_s}{\text{ = + }}\dfrac{1}{2}{\text{ and - }}\dfrac{1}{2}$
Thus on observing each options we can see that, for a given electron the set of ${\text{1, 1, 1, + }}\dfrac{1}{2}$ is not applicable as we cannot have azimuthal number equal to $1$ . For $n{\text{ = 1}}$ the value of an azimuthal quantum number can have value only $0$ . Thus the correct option is $(i){\text{ 1, 1, 1, + }}\dfrac{1}{2}$ .

Note:
For calculating the various values of a quantum number, we must start with the principal quantum number. With the help of principal quantum numbers we can calculate the values of other quantum numbers easily. Spin quantum tells us about the spin of an electron, whether it is rotating clockwise or anti-clockwise.