Question

Which of the following options is/are correct for a shell having principal quantum number n = 5?

• A. The number of orbitals in the shell is 25
• B. Maximum number of electrons in the $5f$ subshell is 14
• C. Orbital angular momentum of the electron in the $5d$ subshell is $\frac{h\sqrt{5}}{2\pi }$
• D. The maximum number of electrons in the shell is 50

Answer 1

Answer: (A), (B), (D)

The correct options are
A The number of orbitals in the shell is 25
B Maximum number of electrons in the $5f$ subshell is 14
D The maximum number of electrons in the shell is 50

Principal quantum number is denoted by 'n'.
Number of orbitals in the shell = $n^2$
So, for n = 5, number of orbitals = $5^2$ = 25

The maximum number of electrons in $5f$ subshell is given by $2(2l+1)$ where, $l$ = azimuthal quantum number.
For $5f$ subshell, $l$ = 3, maximum number of electrons = $2(2\times 3+1$) = 14

Orbital angular momentum = $\frac{h}{2\pi }\sqrt{l}(l+1)$.
So, for $l$ = 2 momentum will be $\frac{h}{2\pi }\sqrt{6}$

Maximum number of electrons in a shell = $2n^2$
For n = 5, maximumnumber of elelctrons = $2(5{)}^2$ = 50