Question

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

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

Answer 1

Answer: (D)

The sets of the quantum numbers and the corresponding orbitals are as shown below.
a) $n=3,1=0$ means $3s-$ orbital
b) $n=3,1=1$ means $3p-$ orbital
c) $n=4,1=2$ means $4d-$ orbital
d) $n=4,1=0$ 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 $(n=4,1=2,m=1,s=+1/2)$ represents the highest energy of an atom.