Atom Absorbing and Emitting Photons

[blue_lilly]

Homework Statement

Consider a pretend atom for which the electrons can be in anyone 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]​

Homework 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

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 ; can't​

2) 4.00 E-19 J ; can't​

3) 1.40 E-18 J ; can't​

4) 6.00 E-19 J ; can​

5) 2.00 E-19 J ; can't​

But those answers are incorrect.

Any help would be greatly appreciated.

 

[TSny]

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:

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​

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.

 

[lightgrav]

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?

 

[TSny]

TSny goofed up about -1.4 E-18J J (it _is _ the most negative, at -14.0 E-19 J).

Indeed I did. Thanks lightgrav!

 

[HalfLostAndSearching]

Thank you for your response.

I would like to clarify a few things about this problem. First, the energy levels of an atom are usually represented by the letter "n" instead of letters like A, B, C, D. So let's use n instead of A, B, C, D for the energy levels.

Also, the energy levels of an atom are usually measured in units of electron volts (eV) rather than joules (J). So let's use eV instead of J for the energy values.

Now, let's arrange the energy levels on a graph with n on the x-axis and energy (in eV) on the y-axis. The graph would look like this:

n | -1.4 | -0.8 | -0.5 | -0.3
---------------------------------------------
E | -1.4 | -0.8 | -0.5 | -0.3

Note that the energy levels are negative because they represent the energy required to remove an electron from the atom.

Now, let's answer the 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]

Correct Answers:
From level B to level A - Emitted
From level D to level C - Absorbed
From level A to level C - Absorbed
From level C to level B - Emitted

B) What is the energy of the photon absorbed in the transition from level A to level C?
To answer this, we need to find the difference in energy between level A and level C. From the graph, we can see that the energy difference is 0.9 eV. So the energy of the absorbed photon would be 0.9 eV.

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/