The energy (in joules) of an electron energy level in the Bohr atom is given by the expression: En = -2.179 x 10-18/n2 J where n is the principal quantum number for the energy level. What is the frequency in Hz of the electromagnetic radiation absorbed when an electron is raised up from level with n = 3 to that with n = 4?
See your post above.
To find the frequency (ν) of the electromagnetic radiation absorbed when an electron moves from level n = 3 to n = 4, we can use the formula:
ΔE = hf
Where ΔE is the change in energy, h is Planck's constant, and f is the frequency.
Since the energy levels in the Bohr atom are given by the expression:
En = -2.179 x 10^-18 / n^2 J
We can calculate the change in energy (ΔE) as follows:
ΔE = E_final - E_initial
ΔE = (-2.179 x 10^-18 / 4^2) - (-2.179 x 10^-18 / 3^2)
Now, we can substitute this value into the formula to find the frequency:
hf = ΔE
f = ΔE / h
Using the given value of Planck's constant (h = 6.626 x 10^-34 J∙s), we can calculate the frequency (f) in Hz.
To find the frequency of the absorbed electromagnetic radiation, we can use the equation:
E = h * v
where E is the energy of the absorbed radiation, h is Planck's constant (6.626 x 10^-34 J·s), and v is the frequency of the radiation.
First, we need to calculate the energy difference between the two energy levels.
For n = 3, the energy is given by:
E1 = -2.179 × 10^-18 / (3^2) J
For n = 4, the energy is given by:
E2 = -2.179 × 10^-18 / (4^2) J
To find the energy difference, we subtract the lower energy level from the higher energy level:
ΔE = E2 - E1
Substituting the values, we have:
ΔE = [-2.179 × 10^-18 / (4^2)] - [-2.179 × 10^-18 / (3^2)] J
Calculate the value of ΔE.
Once we have the energy difference, we can rearrange the equation E = h * v to solve for the frequency, v:
v = E / h
Substitute the value of ΔE into the equation to find the frequency, v.