The energies, E, for the first few states of an unknown element are shown here in arbitrary units.
n 1 2 3 4 0
E -63 -27 -12 9 infinity
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 Results
A 63 ?
B 51
C 47
D 36
The electron is in n=1 now and if the energy is right it will move to one of the upper energy levels. Take the difference between n=1 and the others; ;i.e.,
n=1 = -63
n=2 = -27
-63-(-27) = -36 so it will take 36 units to move to n = 2. D has 36 units so D will move to n = 2. The others are done the same way. Don't worry about the - sign; that occurs because of convention.
To determine the result of each photon absorption by an n=1 electron, we need to compare the energy of the photon to the energy levels of the electron.
The given energies for the first few states of the unknown element are:
n E (in arbitrary units)
1 -63
2 -27
3 -12
4 9
0 infinity
Based on this information, we can determine the result for each photon absorption:
A photon with an energy of 63 units:
This photon has the same energy as the difference between the n=1 and n=0 energy levels (-63).
Therefore, the absorption of this photon would result in the electron transitioning from n=1 to n=0. (?)
A photon with an energy of 51 units:
This photon does not match exactly with the energy differences between any two energy levels of the electron.
Therefore, this photon would not be absorbed by the n=1 electron.
A photon with an energy of 47 units:
This photon does not match exactly with the energy differences between any two energy levels of the electron.
Therefore, this photon would not be absorbed by the n=1 electron.
A photon with an energy of 36 units:
This photon has the same energy as the difference between the n=2 and n=1 energy levels (-27 - (-63) = 36).
Therefore, the absorption of this photon would result in the electron transitioning from n=1 to n=2.
In summary:
- Photon A (63 units) would result in the electron transitioning from n=1 to n=0.
- Photon B (51 units) would not be absorbed by the n=1 electron.
- Photon C (47 units) would not be absorbed by the n=1 electron.
- Photon D (36 units) would result in the electron transitioning from n=1 to n=2.
To determine the absorption or lack thereof of each photon by an n=1 electron, we need to consider the energy differences between the photon energy and the available energy levels of the electron.
In this case, we have the energies of the electron states given as:
n 1 2 3 4 0
E -63 -27 -12 9 infinity
Let's start by calculating the energy differences for each photon:
Photon A with energy 63:
The energy difference between n=1 and n=0 is 63 - (-63) = 126. This means that an electron in the n=1 state can absorb a photon with an energy of 63.
Photon B with energy 51:
The energy difference between n=2 and n=1 is -27 - (-63) = 36. This means that an electron in the n=1 state cannot absorb a photon with an energy of 51 because it is not equal to the energy difference.
Photon C with energy 47:
The energy difference between n=2 and n=1 is -27 - (-63) = 36. This means that an electron in the n=1 state cannot absorb a photon with an energy of 47 because it is not equal to the energy difference.
Photon D with energy 36:
The energy difference between n=2 and n=1 is -27 - (-63) = 36. This means that an electron in the n=1 state can absorb a photon with an energy of 36.
So, to match each photon to the result of its absorption (or lack thereof) by an n=1 electron:
A - 63: The electron absorbs the photon.
B - 51: The electron does not absorb the photon.
C - 47: The electron does not absorb the photon.
D - 36: The electron absorbs the photon.
Please note that these calculations are based on the given energy levels, and the element is unknown in this case.