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?

Respuesta :

Answer:

Explanation:

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

(a) The highest as well as the minimum frequency will be "n=3 to n=2 to n=1".

(b) The ionization energy will be "900 kJ.mol".

(c) The shortest wavelength will be "221.155 nm".

(a) Because all electronically stages below n=3 have almost the similar energy, there'll be no energy development inside this electronic configuration from n=3 to n=1.

(b)

Ionization energy of ground state will be:

= [tex]15\times 10^{-19} \ J/electron[/tex]

= [tex]15\times 10^{-19}\times 6.02\times 10^{23} \ J/mol[/tex]

= [tex]90\times 10^4[/tex]

= [tex]900 \ kJ/mol[/tex]

(c)

→ The shortest wavelength will be:

= [tex](11-2)\times 10^{-19} \ J[/tex]

= [tex]9\times 10^{-19} \ J[/tex]

= [tex]\frac{9\times 10^{-19}}{1.6\times 10^{-19}}[/tex]

= [tex]5.625 \ eV[/tex]

= [tex]221.155 \ nm[/tex]

Thus the above answers are correct.

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