Question on structure of atom

[Dhamnekar Winod]

An x-ray photoelectron spectroscopy experiment with an unidentified element, X, displays an emission spectrum with four distinct kinetic energies:
5.9 × 10⁻¹⁷ J,2.53 × 10⁻¹⁸ , 2.59 × 10⁻²⁰ J, 2.67 × 10⁻²⁰ (Assume the incident light has sufficient energy to eject any electron in the atom.)

(a)Name all of the possible ground state atoms that could yield this spectrum.

(b)Calculate the binding energy of an electron in the 2p orbital of element X if the x-rays used for the spectroscopy experiment had an energy of \(2.68×10^{−16} J \)

(c)Consider both the filled and unfilled orbitals of element X. Determine the number of: (1) total nodes in a 4d orbital (2)angular nodes in the \(2p_y\) orbital (3)degenerate 5p orbitals

Answers:
(a) 4 orbitals: 1s,2s,2p,3s
Unknown atom: Na or Mg

(b) 2p orbital: 2nd lowest work function, 2nd highest Kinetic Energy= 2.53 × 10⁻¹⁸ J

Energy of photon= work function (ϕ) + KE ⇒ ϕ= Energy of photon-KE ⇒ ϕ= 2.68 × 10⁻¹⁶ - 0.0253 × 10⁻¹⁶ =\(2.6\underline{5}47\) × 10⁻¹⁶ J , Hence, BE= ϕ= -2.65 × 10⁻¹⁶ J

(c) Total nodes in 4d orbitals =3 nodes
Angular nodes in 2py orbitals =1
Degenerate 5p orbtals: 5px, 5py, 5pz = 3 orbitals