The following values are the only allowable energy levels of a hypothetical one-electron atom:

E₆ = - 2 x 10⁻¹⁹ J

E₅ = - 7 x 10⁻¹⁹ J

E₄ = - 11 x 10⁻¹⁹ J

E₃ = - 15 x 10⁻¹⁹ J

E₂ = - 15 x 10⁻¹⁹ J

E₁ = - 15 x 10⁻¹⁹ J

(a) If the electron were in the n = 3 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted? (b) What is the ionization energy (in kJ/mol) of the atom in its ground state? (c) If the electron were in the n = 4 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?

Question

Eddie May

Chemistry

7 June, 13:18

The following values are the only allowable energy levels of a hypothetical one-electron atom:

E₆ = - 2 x 10⁻¹⁹ J

E₅ = - 7 x 10⁻¹⁹ J

E₄ = - 11 x 10⁻¹⁹ J

E₃ = - 15 x 10⁻¹⁹ J

E₂ = - 15 x 10⁻¹⁹ J

E₁ = - 15 x 10⁻¹⁹ J

(a) If the electron were in the n = 3 level, what would be the highest frequency (and minimum wavelength) of radiation that could be emitted? (b) What is the ionization energy (in kJ/mol) of the atom in its ground state? (c) If the electron were in the n = 4 level, what would be the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization?

+5

Answers (1)

Know the Answer?

Micah Espinoza · Answer 1

a) All the electronic levels below n = 3 have same energy so there will not be any evolution of energy in electronic transition from n=3 to n=2 or to n = 1.

b) Ionisation energy of ground state = 15 x 10⁻¹⁹ J per electron

= 15 x 10⁻¹⁹ x 6.02 x 10²³ J / mol

= 90 x 10⁴ J/mol

= 900 kJ / mol

c) the shortest wavelength (in nm) of radiation that could be absorbed without causing ionization will correspond to n = 4 to n = 6

= (11 - 2) x 10⁻¹⁹ J

= 9 X 10⁻¹⁹ J

= 9 X 10⁻¹⁹ J / 1.6 X 10⁻¹⁹

= 5.625 eV

= 1244 / 5.625 nm

= 221.155 nm