Question

Which one of the following sets of quantum numbers represents the highest energy level in an atom?

• A. $n=4,l=0,m=0,s=+1/2$
• B. $n=3,l=1,m=1,s=+1/2$
• C. $n=3,l=2,m=-2,s=+1/2$
• D. $n=3,l=0,m=0,s=+1/2$

Answer 1

The correct option is C $n=3,l=2,m=-2,s=+1/2$

For $(n,l,m,s)=(4,0,0,+1/2)$ electron in 4s shell

For $(n,l,m,s)=(3,1,1,+1/2)$ electron in 3p shell

For $(n,l,m,s)=(3,2,-2,+1/2)$ electron in 3d shell

For $(n,l,m,s)=(3,0,0,+1/2)$ electron in 3s shell

We know that electrons in various shells are filled in as:

$1s<2s<2p<3s<3p<4s<3d<4p<5s$

Highest energy level in an atom is in 3d shell $(n,l,m,s)=(3,2,-2,+1/2)$