Question

The ground state energy of hydrogen atom is -13.6 eV. Consider an electronic state $\Psi$ of $He^+$ whose energy, azimuthal quantum number and magnetic quantum number are -3.4 eV, 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 experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge

Answer 1

Answer: (A), (B)

$\#$ $ -3.4=\frac{-13.6\times4}{n^{2}}$
$n=4$
$\#$ $\ell=2$
$\#\,m=0$
Angular nodes $= l = 2$
Radial nodes $=\left(n-\ell -1\right)=1$
$n\,\ell=4d$ state