Final answer:
To calculate the wavelength of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 2 state, we can use the formula: wavelength = (c * h) / E. Substituting the values into the formulas, we find that the wavelength is approximately 434.0 nm.
Step-by-step explanation:
To calculate the wavelength of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 2 state, we can use the formula:
wavelength = (c * h) / E
where c is the speed of light, h is Planck's constant, and E is the energy difference between the two states. We can calculate the energy difference using the formula:
E = R_H * ((1/n1^2) - (1/n2^2))
where R_H is the Rydberg constant and n1 and n2 are the quantum numbers of the initial and final states, respectively. Substituting the values into the formulas and converting the wavelength to nanometers, we find that the wavelength is approximately 434.0 nm.