The energies, E, for the first few states of an unknown element are shown here in arbitrary units:
n= 1, E=-96
n=2, E=-45
n=3, E=-21
n=4, E=-15
...,...
infinity, 0
A gaseous sample of this element is bombarded by photons of various energies (in these same units). Match each photon to the result of its absorption (or lack thereof) by an n=1 electron.
Photon/Energy:
A/96
B/75
C/69
D/51
Possible answers:
n=1 to n=2
n=1 to n=3
n=1 to n=4
electron ejected
not absorbed
I think C is n=1 to n=3 but im not sure
No, that answer is not right. I make a chart like this.
infinity, 0
n=4, E=-15
n=3, E=-21
n=2, E=-45
n= 1, E=-96
Now you want to determine the difference between energy levels. I start with n = 1 and go to n = 2. That would be the first possible absorption of a photon. That difference is 96 - 45 = 51. I look at the answers and 51 says that is answer D and the absorption of N = 1 to N = 2
Next might be n = 1 to n = 3. That difference is 96-21 = 75. I pick answer B for the absorption n = 1 to n = 3.
When I've finished with n = 1 to n = ?? then I go to the differences between n - 2 and n = 3, 4, infinity, etc. I'll leave the others for you.
To determine which states a photon can excite an n=1 electron to, we need to compare the energy of the photon to the energy differences between different states of the unknown element.
The energy differences between the states can be calculated by subtracting the energy of one state from the energy of another. For example, the energy difference between n=1 and n=2 is:
ΔE(1, 2) = E(2) - E(1) = -45 - (-96) = 51
Using the same approach, we can calculate the energy differences for other state transitions:
ΔE(1, 3) = E(3) - E(1) = -21 - (-96) = 75
ΔE(1, 4) = E(4) - E(1) = -15 - (-96) = 81
Based on these calculations, we can now compare the energy of each photon to the energy differences:
Photon A has an energy of 96, which matches the energy difference ΔE(1, 2) = 51, indicating it can excite the n=1 electron to n=2. So, the answer can be n=1 to n=2.
Photon B has an energy of 75, which matches the energy difference ΔE(1, 3) = 75 exactly, indicating it can excite the n=1 electron to n=3. So, the answer can be n=1 to n=3.
Photon C has an energy of 69, which does not match any of the energy differences calculated. Therefore, the n=1 electron will not absorb this photon, and the answer can be not absorbed.
Photon D has an energy of 51, which matches the energy difference ΔE(1, 2) = 51, indicating it can excite the n=1 electron to n=2. So, the answer can be n=1 to n=2.
Based on these comparisons, the correct matches between photons and the result of their absorption (or lack thereof) by an n=1 electron are:
Photon A/96 = n=1 to n=2
Photon B/75 = n=1 to n=3
Photon C/69 = not absorbed
Photon D/51 = n=1 to n=2
Therefore, your initial identification was incorrect. Photon C with an energy of 69 does not match any energy difference, hence it will not be absorbed by the n=1 electron.