Question

The ground state energy of hydrogen atom is $-13.6eV$. Consider an electronic state $\Psi$ of $H{e}^{+}$ whose energy, azumuthal quantum number and magnetic quantum number are $-3.4eV$, $2$ and $0$, respectively. Which of the following statement(s) is/are true for the state $\Psi$?

• A. It is a $4d$ state
• B. It has 2 angular nodes
• C. It has 3 radial nodes
• D. The nuclear charge experience by the electron in this state is less than $2e$, where e is the magnitude of the electronic charge.

Answer 1

Answer: (A), (B)

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

Given, energy of $H{e}^{+}$ is -13.6 eV
$\therefore -3.4=\frac{-13.6\times 2^2}{n^2}$
$\Rightarrow n=4$
Again azimuthal quantum number $l=2$
a) It is a 4d state.
b) Since $l=2$, it has two angular nodes.
c) Number of radial nodes $=n-l-1=4-2-1=1$
d) Since we are considering $H{e}^{+}$ ion, thus nuclear charge experienced by the electron in this state is +2e