Final answer:
The energy of the light emitted in a transition from ni=5 to nf=2 is calculated using the Rydberg formula, where R is the Rydberg constant, Z is the atomic number (1 for hydrogen), and ni and nf are the initial and final quantum numbers.
Step-by-step explanation:
The energy of the light emitted during a transition from the state ni=5 to the state nf=2 in an atom can be calculated using the Rydberg formula for the energy levels of an electron in a hydrogen-like atom:
E = -RZ2 (1/nf2 - 1/ni2)
where R is the Rydberg constant (approximately 2.18 × 10-18 J), Z is the atomic number of the atom (Z=1 for hydrogen), ni is the initial quantum number, and nf is the final quantum number. The energy of the emitted photon is the difference in energy between the two states. For a hydrogen atom, the transition from ni=5 to nf=2 would release a photon with a discrete energy value unique to that transition.
To find this particular energy value, we would plug into the formula the values of Z=1, nf=2, and ni=5. The calculated energy would then represent the energy of the emitted photon.