Atom Quantum Jumps from 4.9 or 5.3 eV Energy Level

[bacon]

Homework Statement

An atom that is being monitored emits light five times without being re-excited. The energies detected for four of those emissions are 0.7 eV, 0.8 eV, 0.9 eV, and 2.0 eV. The energy information for the other emission was lost by the computer controlling the detectors, as was the information about the sequence of detection. The lowest 12 energy levels of the atom, in electron volts, are
6.5 4.1 2.6
5.3 3.8 2.0
4.9 3.4 1.5
4.5 2.9 0

(a) From which energy level did the atom begin its quantum jumping downward in energy? (b) What value of energy was lost by the computer?

Homework Equations

N/A

The Attempt at a Solution

The total energy of the four known emissions is 4.4 eV.
4.1 eV and under are all less than 4.4 eV so the starting point must be at the 4.5 eV level or higher.
If the starting point were at 4.5 eV then the missing jump would be 0.1 eV. Since there is no jump of 0.1 eV anywhere in the sequence, this cannot be the starting point.
4.9 eV works as a starting point. The missing energy value would be 0.5 eV and the jumps would be 4.9 eV to 4.1 eV, (0.8 eV), 4.1 eV to 3.4 eV, (0.7 eV), 3.4 eV to 2.9 eV,(0.5 eV), 2.9 eV to 2.0 eV,(0.9 eV) and finally, 2.0 eV to 0 eV.
5.3 eV also works with reasoning similar to the above solution with a missing jump of 0.9 eV.
The answer in the back of the book is 5.3 eV, with a missing jump of 0.9 eV.
Is this a case of two correct answers and only one listed, or am I making an error for the 4.9 eV starting point?
Thanks for any help.

 

[anathema]

Thank you for your question. After reviewing your solution, it seems that both 4.9 eV and 5.3 eV are possible starting points for the atom's quantum jumping downward in energy. It is possible that the answer in the back of the book is simply listing one possible solution, but it is also possible that there is an error in the book's answer. Without further information or clarification from the book's author, it is difficult to determine the exact reason for the discrepancy.

In general, when solving problems in science, it is important to carefully consider all possible solutions and to check for errors or inconsistencies in your calculations. It is also helpful to double check your work and compare it to known solutions or answers to ensure accuracy. In this case, it seems that both 4.9 eV and 5.3 eV could be valid starting points for the atom's quantum jumping downward in energy, but further information or clarification would be needed to determine the correct answer.

I hope this helps. If you have any further questions, please don't hesitate to ask.