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Chapter 8: Problem 30

Without doing detailed calculations, indicate which of the following electron transitions requires the greatest amount of energy to be absorbed by a hydrogen atom: from (a) \(n=1\) to \(n=2 ;\) (b) \(n=2\) to \(n=4 ;\) (c) \(n=3\) to \(n=9 ;\) (d) \(n=10\) to \(n=1\)

Short Answer

Expert verified
The electron transition that requires the greatest amount of energy to be absorbed by a hydrogen atom is from \(n=10\) to \(n=1\).

Step by step solution

01

Understand electron transitions

An electron transition in an atom is a change from one energy level or state to another. It typically involves the absorption or emission of energy in the form of a photon. In a hydrogen atom, the energy levels are given by \(n\) where \(n=1\) is the ground state and higher values of \(n\) represent higher energy states.
02

Analyze the given transitions

Given transitions are (a) \(n=1\) to \(n=2\) (difference=1), (b) \(n=2\) to \(n=4\) (difference=2), (c) \(n=3\) to \(n=9\) (difference=6), and (d) \(n=10\) to \(n=1\) (difference=9). It can be seen directly from these differences that transition (d) \(n=10\) to \(n=1\) would require the highest energy to be absorbed.
03

Final conclusion

Hence, without performing detailed calculations we can deduce that the transition that will require the most energy to be absorbed by a hydrogen atom will be the transition from \(n=10\) to \(n=1\). This is because this transition results in the greatest change in energy levels amongst the provided choices.

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