The energies, E, for the first few states of an unknown element are shown here in arbitrary units.
n 1 E -11
n 2 E -5
n 3 E -2
n 4 E -1
n ... E ...
n infinite E 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/11
B/9
C/8
D/6
Choices:
n=1 to n=2
n=1 to n=3
n=1 to n=4
electron ejected
not absorbed
In order to get 11, I need to go from 11 to zero. Zero is infinity which means the electron was ejected (ionized).
To get 9 I need 2 to 11 and that is n = 1 to n = 3. Can you take it from here?
I need help with the rest.
What is C/8? not absorbed?
Is D/8 n=1 to n=2?
To determine the result of the absorption (or lack thereof) of each photon by an n=1 electron, we need to compare the energy of each photon with the energy differences between different energy states.
Let's analyze the given energies for the first few states of the unknown element:
n=1 E -11
n=2 E -5
n=3 E -2
n=4 E -1
The energy difference between two consecutive states can be calculated by subtracting the lower energy from the higher energy.
For example:
n=2 E - n=1 E = -5 - (-11) = 6
n=3 E - n=2 E = -2 - (-5) = 3
n=4 E - n=3 E = -1 - (-2) = 1
Now, let's match each photon to the result of its absorption (or lack thereof) by an n=1 electron using the given photon energies:
A/11
B/9
C/8
D/6
Photon A has an energy of 11. The only energy transition that can accommodate this energy is from n=1 to n=2, with an energy difference of 6. Therefore, photon A will be absorbed, causing an n=1 to n=2 transition.
Photon B has an energy of 9. There are no energy differences that match this value. Therefore, photon B will not be absorbed.
Photon C has an energy of 8. The energy difference from n=1 to n=2 is 6, which is less than the energy of photon C. However, the energy difference from n=1 to n=3 is 3, which is greater than the energy of photon C. Therefore, photon C will be absorbed, causing an n=1 to n=3 transition.
Photon D has an energy of 6. We already know that the energy difference from n=1 to n=2 is 6. Therefore, photon D will be absorbed, causing an n=1 to n=2 transition.
Based on the analysis above, we can match each photon to the result of its absorption (or lack thereof) by an n=1 electron as follows:
A/11: n=1 to n=2
B/9: not absorbed
C/8: n=1 to n=3
D/6: n=1 to n=2
To determine which photon is matched to the result of its absorption (or lack thereof) by an n=1 electron, we need to understand the energy levels of the unknown element and compare them with the energies of the photons.
Looking at the given energies for the first few states of the element, we see that as the value of n increases, the energy level becomes less negative and approaches zero. This indicates that the energy levels become closer together as n increases, and the difference in energy between consecutive levels decreases.
Now, let's consider the energy differences between the states:
- The energy difference between n=1 and n=2 is 11 - (-11) = 22.
- The energy difference between n=1 and n=3 is 5 - (-11) = 16.
- The energy difference between n=1 and n=4 is 2 - (-11) = 13.
Given the energies of the photons A, B, C, and D, let's compare them with the energy differences:
- Photon A has an energy of 11, which matches the energy difference between n=1 and n=2 (22). Therefore, Photon A corresponds to the transition from n=1 to n=2.
- Photon B has an energy of 9. Since there is no energy difference that matches exactly 9, it means the photon's energy is not suitable for any transition from n=1. Therefore, Photon B is not absorbed by the n=1 electron.
- Photon C has an energy of 8, which is less than the energy difference between n=1 and n=3 (16). Thus, Photon C is not capable of exciting the n=1 electron to a higher energy level. Therefore, Photon C is not absorbed.
- Photon D has an energy of 6, which is even less than the energy difference between n=1 and n=4 (13). Similar to Photon C, Photon D does not possess enough energy to excite the n=1 electron. Therefore, Photon D is also not absorbed.
To summarize:
Photon A (energy of 11) corresponds to the transition from n=1 to n=2.
Photons B, C, and D (energies of 9, 8, and 6, respectively) are not absorbed by the n=1 electron.
Thus, the matching between the photons and the result of their absorption by an n=1 electron is as follows:
Photon A is absorbed (n=1 to n=2).
Photons B, C, and D are not absorbed.