Question

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

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

Answer 1

The correct option is C $n=4,l=2,m=1,s=+1/2$

The sets of the quantum numbers and the corresponding orbitals are as shown below.
$a)n=3,l=0$ means $3s-$ orbital
$b)n=3,l=1$ means $3p-$ orbital
$c)n=4,l=2$ means $4d-$ orbital
$d)n=4,l=0$ means $4s-$ orbital
Increasing order of energy among three orbitals is $3s<3p<4s<4d$
$\therefore 4d$ has highest energy.
Hence, the set c of quantum numbers ($n=4,l=2,m=1,s=+1/2$) represents the highest energy of an atom.