Final answer:
The energy change in the second Balmer transition of the hydrogen spectrum is not the same as the given energy change in the first Lyman transition.
Step-by-step explanation:
The Lyman series in the hydrogen spectrum refers to the set of transitions where an electron in a hydrogen atom jumps from a higher energy level to the ground state (energy level 1). The first Lyman transition corresponds to a jump from energy level 2 to level 1. The energy change for this transition is given as ΔE = 10.2 eV.
To determine which of the given options has the same energy change in the second Balmer transition, we need to calculate the energy change for that transition. The second Balmer transition corresponds to a jump from energy level 4 to level 2. We can use the equation ΔE = -13.6 eV * (1/nfinal2 - 1/ninitial2) to calculate the energy change. Plugging in the values for the Balmer transition gives:
ΔE = -13.6 eV * (1/22 - 1/42) = 13.6 eV * (1/4 - 1/16) = 9.36 eV
Therefore, the energy change in the second Balmer transition is 9.36 eV, which is not the same as the given energy change of 10.2 eV. None of the given options match the energy change in the second Balmer transition.