Final answer:
To calculate the transition wavelength between two quantum states in a hydrogen-like atom, the Rydberg formula is typically used. However, the options provided suggest a missing formula relation. Without more context or the correct formula, we cannot select an accurate answer from the listed options.
Step-by-step explanation:
The student has asked to calculate the wavelength for the transition between two states in a hydrogen atom. To solve this, we use the Rydberg formula for hydrogen-like atoms, which relates the energy difference between orbits to the wavelength of the emitted or absorbed light.
The energy levels of hydrogen are given by En = -13.6 eV/n^2, where n is the principal quantum number. So, we calculate the energies of the two states first and then find the energy difference (ΔE) between them. Next, we use the relation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength.
However, we need more specific information or formulae from the student to give the correct wavelength for the options provided (A through D), as the given options suggest a missing formula or concept that should relate mass m with the Planck constant h and produce the correct wavelength of the transition.
Without additional context or the correct formula, we cannot confidently provide an accurate answer from the options listed. To complete this problem, we need the exact relationship between the quantum states and their corresponding wavelengths, which typically involves the Rydberg constant and the principal quantum numbers of the initial and final states.