JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Atomic Structure

For a shell of principal quantum number $n$, the azimuthal quantum number $l$ runs from 0 to $n-1$, and each subshell holds $2l+1$ orbitals, so the total number of orbitals is ${\sum }_{l=0}^{n-1}(2l+1)=n^2$ — 1 for $n=1$, 4 for $n=2$, 9 for $n=3$, and so on. Statement I is correct. Within any subshell of azimuthal quantum number $l$, the magnetic quantum number $m_l$ takes the $(2l+1)$ values $-l,\dots ,0,\dots ,+l$, each fixing a distinct spatial orientation of that orbital. Statement II is correct too. Both statements hold.