Question

List - I	List - II
I) ${\Psi }^2$ depends only upon distance	a) p-orbitals
II) ${\Psi }^2$ depends upon distance and on one direction	b) d-orbital
III) ${\Psi }^2$ depends upon distance and on two directions	c) f-orbital
IV) ${\Psi }^2$ depends upon distance and on three directions	d) s-orbitals

• A. I-d, II-c, III-b, IV-a
• B. I-c, II-b, III-a, IV-d
• C. I-d, II-a, III-b, IV-c
• D. I-d, II-a, III-c, IV-b

Answer 1

Answer: (C)

I-d, II-a, III-b, IV-c

Azimuthal quantum number $l$ describes the shape of orbitals occupied by the electrons.
1) When $l=0$ the orbital is spherical, i.e., $s$ is the orbital. When $l=0$, the magnetic quantum number $m=0$, so there is only one such orbital for each value of $n$. Then, ${\Psi }^2$ depends only on distance $r$ from the nucleus and is same in all directions.

2) When $l=1$, the orbital is $p$ orbital. When $l=1$, the magnetic quantum number $m=(2l+1)=3(-1,0,+1)$. There are therefore three orbitals which are identical in energy, shape and size, which differ only in their direction in space. So, for this group, solution to wave equation ${\Psi }^2$ depends both on distance from nucleus $r$ and only one direction in space $(x,y,z)$. These three solution to wave equation may be written as :
${\Psi }_x=f\left(r\right).f\left(x\right)$
${\Psi }_y=f\left(r\right).f\left(y\right)$
${\Psi }_z=f\left(r\right).f\left(z\right)$

3) When $l=2$, the orbital is $d$ orbital. When $l=2$, the magnetic quantum number $m=(2l+1)=5(-2,-1,0,+1,+2)$. There are therefore five orbitals. So, for this group, solution to wave equation ${\Psi }^2$ depends both on distance from nucleus $r$ and any two directions in space $(x,y,z)$. These solutions to wave equation may be written as for example, ${\Psi }_x=f\left(r\right).f\left(x\right).f\left(y\right)$.

4) When $l=3$, the orbital is $f$ orbital. When $l=3$, the magnetic quantum number $m=(2l+1)=7(-3,-2,-1,0,+1,+2,+3)$. There are therefore seven orbitals. So, for this group, solution to wave equation ${\Psi }^2$ depends both on distance from nucleus $r$ and three direction in space $(x,y,z)$. These solution to wave equation may be written as for example ${\Psi }_x=f\left(r\right).f\left(x\right).f\left(y\right).f\left(z\right)$.