How do I solve this light/energy problem?

Question

In the investigation of the electronic absorption spectrum of a particular element, it is found that a photon having a wavelength  of 500nm provides just enough energy to promote an electron from the second quantum level to the third. From this information, we can deduce:

 

A. The energy of the n=2 level

B. The energy of the n=3 level

C. The sum of the energies of n=2 and n=3

D. The difference in the energies between n=2 and n=3

E. All of the above

Answer 1

Let:

• Ep = the energy of the photon = hc/λ  This quantity is known)
• E2 = the energy of level n=2
• E3 = the energy of level n=3

 

A.  Knowing Ep tells us nothing about E2

B.  All we know about E3 is that E3 = E2 + Ep, but we still don't know E2

C.  E2 + E3 = E2 + E2 + Ep = 2E2 + Ep.  Still don't know E2

D.  E3 - E2 = E2 + Ep - E2 = Ep = hc/λ.  Aha, we know Ep so we know the difference in energy between E2 and E3.

E.  Don't know E2 or E3

 

Answer is D.

 

Answer 2

Choice D. The wavelength corresponds to a specific quantized amount of energy that we are told is enough to excite from the second energy level to the third, which means that amount of energy is the difference between the two levels.