Answer:
1 ---> 3
Step-by-step explanation:
The energy released during a transition in a hydrogen atom depends on the difference in energy between the initial and final states. This energy difference is given by the formula:
ΔE = -Rhc[(1/ni^2) - (1/nf^2)]
where R is the Rydberg constant, h is Planck's constant, c is the speed of light, ni is the initial principal quantum number, and nf is the final principal quantum number.
To determine which transition will release the greatest amount of energy, we need to calculate the energy differences for each of the given transitions and compare them.
For 1 ---> 3 transition,
ΔE = -Rhc[(1/1^2) - (1/3^2)] = -Rhc(8/9 - 1) = -Rhc/9
For 3 ---> 5 transition,
ΔE = -Rhc[(1/3^2) - (1/5^2)] = -Rhc(25/225 - 9/225) = -4Rhc/225
For 4 ---> 2 transition,
ΔE = -Rhc[(1/4^2) - (1/2^2)] = -Rhc(4/16 - 1/4) = -3Rhc/16
For 6 ---> 4 transition,
ΔE = -Rhc[(1/6^2) - (1/4^2)] = -Rhc(16/1296 - 36/1296) = -5Rhc/324
From the above calculations, we can see that the transition from 1 to 3 will release the greatest amount of energy, as it has the largest absolute value of energy difference (-Rhc/9). Therefore, the answer is 1 ---> 3 transition.