What is the final energy level of an electron that absorbs energy of 656nm if the electron started at the n=2 level of the hydrogen atom?
1/wavelength = R(1/2^2 - 1/x^2)
R = 1.09737E7
Solve for X.
(NOTE: It may be easier, math wise, to plug in whole numbers, beginning at 3, and see which whole number(3,4,5,6, etc) ends up giving a wavelength of 656E-9m.)
3.03 x 10^-19 J
Is that right?
I didn't interpret the problem that way. I thought the problem was asking us to determine the orbit to which the electron was promoted. It started at n = 2 and I thought it was asking if it was moved to n = 3, n = 4, n= 5, etc. According to my calculations above it will be moved to n = 3.
3.03E-19 J is the energy of the photon of wavelength 656 nm but that isn't the energy level of the n = 3 orbit.
To find the final energy level of an electron that absorbs energy of 656 nm (nanometers), we need to understand the energy levels of the hydrogen atom and the relationship between energy and wavelength.
In the hydrogen atom, the energy levels are described by the equation:
E = -13.6 eV (Z^2 / n^2)
where E is the energy level, Z is the atomic number of the nucleus (which is 1 for hydrogen), and n is the principal quantum number. The principal quantum number n describes the energy level or shell where the electron is located.
The energy associated with a particular wavelength of light is given by the equation:
E = (hc) / λ
where E is the energy in joules, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters.
To begin, we convert the given wavelength from nanometers to meters.
656 nm = 656 x 10^-9 meters.
Now, we can use the energy equation to calculate the energy of a photon that has a wavelength of 656 nm:
E = (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (656 x 10^-9 meters).
Calculate the value of E, which will give you the energy in joules.
Next, we can equate the energy of the absorbed photon to the energy difference between the final and initial energy levels of the electron:
ΔE = E(final) - E(initial).
Since the initial level is n = 2, we can use the energy equation for the hydrogen atom to calculate E(initial):
E(initial) = -13.6 eV (Z^2 / n^2),
E(initial) = -13.6 eV (1^2 / 2^2).
The value of E(initial) will be in electron volts (eV).
Finally, we can solve for E(final):
ΔE = E(final) - E(initial),
E(final) = ΔE + E(initial).
Substitute the calculated values of ΔE and E(initial) into the equation to find E(final).
The value of E(final) will give you the final energy level of the electron in the hydrogen atom. Keep in mind that the energy levels in the hydrogen atom are quantized, so the final energy level will be an integer value corresponding to the principal quantum number (n).