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?

Question

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? (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

Tardigrade Admin · Accepted Answer

# -3.4=(-13.6×4/n2) n=4 # ℓ=2 # m=0 Angular nodes = l = 2 Radial nodes =(n-ℓ -1)=1 n ℓ=4d state

Q. The ground state energy of hydrogen atom is -13.6 eV. Consider an electronic state $Ψ$ of $H e^{+}$ 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 $Ψ$ ?

It is a 4d state

It has 2 angular nodes

It has 3 radial nodes

The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge

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

Q. 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?