Light shines through atomic hydrogen gas that was initially in its ground state.You observe that after awhile much of the hydrogen gas has been excited to its n = 5 state.What wavelength of light entering the gas caused this excitation? (c = 3.00 × 10⁸ m/s,h = 6.626 × 10^-34 J ∙ s,1 eV = 1.60 × 10^-19J) A)110 nm B)91.4 nm C)95.2 nm D)2280 nm

Question

Quizplus · Accepted Answer

The energy difference between the ground state and the n = 5 state is:$$E_5 - E_1 = (-\frac{13.6}{1^2} + \frac{-13.6}{5^2}) eV = 12.09 eV$$The wavelength of light required to excite the hydrogen gas to the n = 5 state is:$$\lambda = \frac{hc}{E_5 - E_1} = \frac{(6.626 	imes 10^{-34} J \cdot s)(3.00 	imes 10^8 m/s)}{12.09 eV 	imes (1.60 	imes 10^{-19} J/eV)} = 95.2 nm$$

Light Shines Through Atomic Hydrogen Gas That Was Initially in Its