(P) If azimuthal quantum number value is 3, the maximum value of spin multiplicity is z.

(Q) If value or principal quantum number is 3, the maximum number or orbitals In the shell will be y. Find the value of $y-x$.

The greatest and minimum spin multiplicities are 8 and 2, respectively, when the azimuthal quantum number is 3, the value. 

The maximum spin multiplicity is, $2S+1=2\times \frac{7}{2}+1=8$.

The maximum number or orbitals In the shell is

$\mathrm{y}={\mathrm{n}}^2$

$\mathrm{y}=3\times 3$

$\mathrm{y}=9$

The value of $y-x$ is 

 $\mathrm{y}-\mathrm{x}=9-8=1$