Question

A hydrogen atom is initially at the ground state and then absorbs energy 13.06 eV. The excited state is unstable, and it tends to finally return to its ground state. 8%

(a) How many possible wavelengths will be emitted as the atom returns to its ground state? (also draw a diagram of energy levels to illustrate your answer)

Answer: (number) ___________

(b) Calculate the longest wavelength emitted.

Answer: _________

Answer 1

energy of excited state = -13.6 eV + 13.06 = - 0.54 eV

so,

E_n = - 13.6 eV / n²

- 0.54 eV = - 13.6 eV / n²

so,

n = 5

The lines are as follows

______________________

Longest wavelength corresponds to transition from n = 5 to n = 4

so,

1/ = R ( 1/ 4² - 1/5² )

1/ = 1.097e7 ( ( 1/ 4² - 1/5² )

1/ = 246825

= 4.05e-6 m