Question

A single electron orbits around a stationary nucleus of charge +Ze, where Z is a constant and e is the magnitude of the electronic charge. It requires 47.2 eV to excite the electron from the second Bohr orbit to the third Bohr orbit.

Find

(a) the value of Z

(b)  energy required to excite the electron from the third to the fourth Bohr orbit.

(c)  wavelength of the electromagnetic radiation required to remove the electron from the first Bohr orbit to infinity.

(d)  kinetic energy, potential energy and angular momentum of the electron in the first Bohr orbit

(e)  the radius of the first Bohr orbit.

(The ionization energy of hydrogen atom = 13.6 eV. Bohr radius = 5.3 x 10¹¹ m)

Answer 1

This atom is hydrogen like

Z = atomic number of the nucleus

E_n = Energy of the electron in the nth orbit = (Z)^² (energy of the electron in the nth orbit of the hydrogen atom) 

= -(Z)² 13.6/n² eV = E₁/n²

where E₁ = Energy of the electron in the 1st Bohr orbit of the given atom.

(c) minimum energy required to remove electron from first orbit = 340 eV

(d) KE of the electron in the 1st orbit

KE₁ = –E₁ = 340 eV; PE₁ = 2E₁ = –680 eV

Angular momentum of the electron in the 1st Bohr orbit

(e) Radius of the 1st Bohr orbit for the given atom