If a hydrogen atom undergoes a transtion from n = 1 (E = 4.17 x 10^-19 J) to n = 3 (E = 8.62 x 10^-19 J), what is the wavelength of the photo absorbed?

Question

Quizplus · Accepted Answer

The energy difference between the two states is the energy of the photon absorbed. First, calculate the energy difference: $E = 8.62 \times 10^{-19} J - 4.17 \times 10^{-19} J = 4.45 \times 10^{-19} J$. Then, use the equation $E = \frac{hc}{\lambda}$ to find the wavelength, $\lambda$, where $h$ is Planck's constant ($6.626 \times 10^{-34} m^2 kg / s$) and $c$ is the speed of light ($3.00 \times 10^8 m/s$). Solving for $\lambda$ gives a wavelength in meters, which can be converted to nanometers (nm) by multiplying by $10^9$. The correct calculation leads to a wavelength in the range of $10^{-7}$ meters, or nanometers, making option A the correct choice.

If a Hydrogen Atom Undergoes a Transtion from N =