Question

The ground state energy of hydrogen atom is $–13.6eV$. Consider an electronic state $\psi$ of $H{e}^{+}$ whose energy, azimuthal quantum number and magnetic quantum number are $-3.4eV,2and0$, respectively. Which of the following statement(s) is(are) true for the state $\psi$ ?

• A. It is a $4d$ state
• B. It has 3 radial nodes
• C. It has 2 angular nodes
• D. All statements are incorrect

Answer 1

Answer: (A), (C)

The correct options are
A It is a $4d$ state
C It has 2 angular nodes

$E_{H{e}^{+}}=-13.6\times \frac{(2{)}^2}{n^2}=-3.4$

$n^2=16$
$n=4$
Quantum number are
$n=4,l=2,m=0$
So, subshell is $d$
Angular node=$l=2$
Radial node =$[n-l-1]=4-2-1=1$