The ground state energy of hydrogen atom is - 13.6   e V . Consider an electronic state Ψ of H e +…

The ground state energy of hydrogen atom is -13.6 eV . Consider an electronic state Ψ 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 Ψ ?
  1. It has 2 angular nodes
  2. It has 3 radial nodes
  3. It is a 4d state
  4. The nuclear charge experienced by the electron in this state is less than 2e , where e is the magnitude of the electronic charge.

Solution

∵EHe+=-13.6z2n2=-13.622n2=-3.4
n2=16
∴n=4
n=4,l=2,m=0 belongs to 4dyz orbital
→ Radial nodes ⇒n-l-1
→ Angular nodes ⇒4-2-1=1
→ Angular nodes ⇒l⇒2
Since He+ is a single e- ion, its nuclear charge experienced.

Asked in: JEE Advanced 2019 (Paper 2)

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