What is the energy of light (in J) emitted by a hydrogen atom when an electron relaxes from the 7 energy level to the 5 energy level?
To calculate the energy of light emitted by a hydrogen atom when an electron transitions between energy levels, we can use the formula:
E = hf
where E represents the energy of the light, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the light.
To determine the frequency of the emitted light, we need to use the formula:
ΔE = hf
where ΔE is the change in energy between the initial and final energy levels.
The energy levels of a hydrogen atom can be calculated using the formula:
En = -13.6/n^2
where En represents the energy of the energy level and n is the principal quantum number.
In this case, the initial energy level (n1) is 7, and the final energy level (n2) is 5. So, we can calculate the change in energy (ΔE) using:
ΔE = E2 - E1 = (-13.6/5^2) - (-13.6/7^2)
Once we have the value of ΔE, we can equate it to hf and solve for the frequency (f):
f = ΔE / h
Finally, we can substitute the frequency (f) into the equation E = hf to find the energy of the light (E).
Note: The energy of light is usually expressed in electronvolts (eV), but you can convert it to joules (J) by using the conversion factor: 1 eV = 1.6 x 10^-19 J.