An electron jumps from energy level 1 to energy level 2 by absorbing a photon of energy 8 eV. What is the most likely energy of the photon that will be emitted by the electron when it moves back down to energy level 1?
2 eV
4 eV
8 eV
12 eV
A.2eV
What goes in comes out.
To determine the energy of the photon emitted by the electron when it moves back down from energy level 2 to energy level 1, we need to understand the concept of energy levels in an atom.
In an atom, electrons occupy different energy levels or shells. These energy levels are quantized, meaning they can only have specific values. When an electron transitions from a higher energy level to a lower energy level, it releases energy in the form of a photon.
The energy of a photon can be calculated using the equation:
E = hf
Where E is the energy of the photon, h is Planck's constant (approximately 6.626 x 10^-34 Joule-seconds), and f is the frequency of the photon.
The relationship between energy and frequency is given by:
E = hf
Where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon.
Since we are given the energy of the photon absorbed by the electron when it moves from energy level 1 to 2 (8 eV), we can calculate the frequency of the absorbed photon using the equation:
E = hf
Rearranging the equation, we get:
f = E / h
Substituting the given values:
f = 8 eV / (6.626 x 10^-34 J·s)
Converting electron volts (eV) to joules (J):
1 eV = 1.6 x 10^-19 J
f = (8 x 1.6 x 10^-19 J) / (6.626 x 10^-34 J·s)
Calculating f:
f ≈ 1.93 x 10^15 Hz
Now, when the electron moves back down to energy level 1, it emits a photon with the same frequency. Using the frequency, we can calculate the energy of the emitted photon using the equation:
E = hf
Substituting the frequency we calculated:
E = (1.93 x 10^15 Hz) x (6.626 x 10^-34 J·s)
Calculating E:
E ≈ 1.28 x 10^-18 J
Finally, we can convert the energy of the emitted photon from joules to electron volts:
1 eV = 1.6 x 10^-19 J
Converting E:
E ≈ (1.28 x 10^-18 J) / (1.6 x 10^-19 J/eV)
E ≈ 8 eV
Therefore, the most likely energy of the photon emitted by the electron when it moves back down to energy level 1 is 8 eV. So the correct option is 8 eV.