1.) In the ground state of the Hydrogen atom, the energy of the electron is E 0

Question

1.) In the ground state of the Hydrogen atom, the energy of the electron is E0 = -13.61 eV. What is the energy of the electron in the ground state of the He+ ion? 2.) What is the energy of the electron in the ground state of the Li++ ion? 3.) The electron in the He+ ion is excited to the n = 2 principal state. What is the energy of the electron now? 4.) What is the energy of the electron in the Li++ ion in the n = 2 principal state? 5.) What is the energy of the electron in the Li++ ion in the n = 3 principal state? 6.) Take element Z = 38 from the periodic table. Ionize it 37 times so that there is only 1 electron left orbiting around the nucleus. What is the ground state energy of the electron? 7.) What is the energy of the electron when it is in the n = 7 principal state in the ion above?

Explanation / Answer

1) E = E0(Z^2 / n^2)

for He , Z = 2

E = (-13.6 ev) (2^2 / 1^2)

E = - 54.4 eV .....Ans

2) for Li , Z = 3

E = (-13.6)(3^2) = -122.4 eV ....Ans

3) E = (-54.4)/2^2 = - 13.6 eV ....Ans

4) E = (-122.4)/2^2 = - 30.6 eV ....Ans

5) E = (-122.4)/3^3 = - 13.6 eV  

6) E = (-13.6)(38^2)/1^2

E = - 19638.4 eV

7) E = - 19638.4 / 7^2 = - 400.8 eV  

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