The first Bohr radius, a₀, is 0.0529 nm and the corresponding energy, E₀, is 13.6 eV. The wavelength of the light emitted as a hydrogen atom undergoes a transition from state n = 3 to n = 2 is about A) 656 nm. B) 486 nm. C) 434 nm. D) 410 nm. E) None of these is correct.

Question

Quizplus · Accepted Answer

The energy of a hydrogen atom in the nth state is given by:$$E_n = -\frac{13.6}{n^2} eV$$The wavelength of light emitted when an electron transitions from state n = 3 to n = 2 is given by:$$\frac{1}{\lambda} = R_H (\frac{1}{n_f^2} - \frac{1}{n_i^2})$$where $R_H$ is the Rydberg constant.Plugging in the values for $n_i$, $n_f$, and $R_H$, we get:$$\frac{1}{\lambda} = (1.097 	imes 10^7 m^{-1}) (\frac{1}{2^2} - \frac{1}{3^2})$$$$\lambda = 656 nm$$Therefore, the correct answer is A) 656 nm.

The First Bohr Radius, A0, Is 0

The First Bohr Radius, A₀, Is 0