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`?

Options

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

A, B

Explanation

The ground state energy of hydrogen atom is given by `E_(n)=(-13.6)/(n^2)`
For hydrogen-like atoms, like `He^(+)`, it is given by `E_(n)=-13.6 Z^2/n^2`
Given that `E_(n)=-3.4eV, so -13.6 ((2)^2)/(n^2)=-3.4 rArr n^2=16 rArr n=4`
Also, given that l=2 and m=0, so that orbital is 4d. The number of radial nodes =n-l-1=4-2-1=1. The number of angular nodes =l=2.