A.) Consider a hypothetical hydrogen-like atom with a ground state energy of -22

Question

A.) Consider a hypothetical hydrogen-like atom with a ground state energy of -22.3 eV. Calculate the energies of the 4th and 6th states in this atom. Enter the energy of the 4th state in the first answer field and the energy of the 6th state in the second energy field.

B.) Calculate the frequency of the spectral line associated with an electron moving from state 8 to state 6 (a (8-6) jump.)

C.) And, what is the frequency of the spectral line associated with an electron moving from state 5 to state 1 (a (5-1) jump.)?

Explanation / Answer

A) E4 = -22.3/4^2 = -1.39 eV

E6 = -22.3/6^2 = -0.619 eV

B) from 8 to 6 energy released is E = E6-E8 = (-22.3/6^2) -(-22.3/8^2)= -0.271 eV

E = h*f = 0.271*1.6*10^-19 = 4.336*10^-20

frequency is f = (4.336*10^-20)/(6.626*10^-34) = 6.54*10^13 Hz

C) from 5 to 1

E5-E1 = (-22.3/5^2)-(-22.3) = 21.408 eV = 21.408*1.6*10^-19 = 3.42528*10^-18 Hz

released frequency is f = (3.42528*10^-18)/(6.626*10^-34) = 5.16*10^15 Hz

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