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Atom Absorbing and Emitting Photons

  1. Apr 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Consider a pretend atom for which the electrons can be in any one of the following energy states:
    Label Energy
    A -1.400×10-18J
    B -8.000×10-19J
    C -5.000×10-19J
    D -3.000×10-19J
    Start by arranging the four levels on a graph, then answer the following questions.

    A) An electron jumps from one energy state to another, as described in each of the statements below. Describe whether a photon is absorbed or emitted in the process.
    From level B to level A [Absorbed/Emitted]​
    From level D to level C [Absorbed/Emitted]​
    From level A to level C [Absorbed/Emitted]​
    From level C to level B [Absorbed/Emitted]​
    Incorrect Answer: 1)Emitted 2)Absorbed 3)Absorbed 4)Absorbed

    B) What is the energy of the photon absorbed in the transition from level A to level C?
    9 E-19J This is the Correct Answer

    C) Label each of the following photons as ones that can or cannot be absorbed by this atom. The value stated is the energy of the photon.
    7.00 E-19 J [Can be Absorbed/ Cannot be Absorbed]​
    4.00 E-19 J [Can be Absorbed/ Cannot be Absorbed]​
    1.40 E-18 J [Can be Absorbed/ Cannot be Absorbed]​
    6.00 E-19 J [Can be Absorbed/ Cannot be Absorbed]​
    2.00 E-19 J [Can be Absorbed/ Cannot be Absorbed]​


    2. Relevant equations
    Energy(Absorbed) = Energy(Final) - Energy(Initial)
    Energy(Emitted) = Energy(Initial) - Energy(Final)
    Absorbs a Photon- when electron moves into a higher energy state
    Emits a Photon- when electron moves into a lower energy state


    3. The attempt at a solution
    A) The problem says that you first need to arrange the 4 energy levels on a graph. The new order I got was:

    B -8.000 E-19 J
    C -5.000 E-19 J
    D -3.000 E-19 J
    A -1.400 E-18 J​
    I then used this new graph to answer the following questions:
    1) From level B to level A ; Starting a B and moving to A means that the electron would be moving to a lower energy state, so this would be Emitted.​
    2) From level D to level C ; Starting a D and moving to C means that the electron would be moving to a higher energy state, so this would be Absorbed.​
    3) From level A to level C ; Starting a A and moving to C means that the electron would be moving to a higher energy state, so this would be Absorbed.​
    4) From level C to level B ; Starting a C and moving to B mean that the electron would be moving to a higher energy state, so this would be Absorbed.​
    This is incorrect!

    B) Photon starts at Energy Level A and moves to Energy Level C
    E-absorbed=EnergyLevelInitial -EnergyLevelFinal​
    E-absorbed=(1.400 E-18) - (5.00 E-19)​
    E-absorbed= (9 E-19 J) This is Correct!

    C) This problem says that the value they will give you is the E-absorbed. So I thought I was just supposed plug that number into the equation:
    Energy(Absorbed) = Energy(Final) - Energy(Initial)​

    But I couldn't figure out what either the Final Energy nor the Initial Energy would be. So instead I used the graph to figure out what levels the atom can possibly absorb:

    B -8.000 E-19 J
    C -5.000 E-19 J
    D -3.000 E-19 J
    A -1.400 E-18 J​
    Initial A Final D ; (1.400 E-18) - (3.000 E-19) = (1.1 E-18)​
    Initial A Final C ; (1.400 E-18) - (5.000 E-19) = (9.0 E-19)​
    Initial A Final B ; (1.400 E-18) - (8.000 E-19) = (6.0 E-19)​
    Initial D Final C ; (3.000 E-19) - (5.000 E-19) = (-2.0 E-19)​
    Initial D Final B ; (3.000 E-19) - (8.000 E-19) = (-5.0 E-19)​
    Initial C Final B ; (5.000 E-19) - (8.000 E-19) = (-3 E-19)​

    And then I compared those numbers to the photons given in the question.
    1) 7.00 E-19 J ; cant ​
    2) 4.00 E-19 J ; cant ​
    3) 1.40 E-18 J ; cant ​
    4) 6.00 E-19 J ; can ​
    5) 2.00 E-19 J ; cant ​
    But those answers are incorrect.

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Apr 23, 2014 #2

    TSny

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    Homework Helper
    Gold Member

    Note that the energies of the levels are negative. So, be careful when you rearrange them in increasing order. For example, which is greater: -3 or -5?

    [EDIT:

    It is standard to arrange the levels such that the lowest energy is at the bottom and the greatest energy is at the top. That way, a photon is emitted when you jump from an upper level in the arrangement to a lower level and a photon is absorbed when you jump from a lower level to a upper level.

    You have it arranged the other way around with greatest energy at the bottom. That should be OK as long as you use the fact that when jumping from a higher energy value to a lower energy value, a photon is emitted.
     
    Last edited: Apr 23, 2014
  4. Apr 23, 2014 #3

    lightgrav

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    Homework Helper

    you SHOULD arrange the electron Energies with the deepest (most negative) on the bottom,
    and keep them in ORDER up to the zero (unbound) level.
    That would be easier if you made all the exponents the same ... even TSny goofed up about -1.4 E-18J J (it _is _ the most negative, at -14.0 E-19 J).
    C) you said that D to C would need -2 E-19 J of Energy absorbed ... what does that negative mean?
    what Energy would C do D need?
     
  5. Apr 23, 2014 #4

    TSny

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    Homework Helper
    Gold Member

    Indeed I did. Thanks lightgrav!
     
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