determine the end value of n in a hydrogen atom transition if the electron starts in n=2 and the atom absorbs a photon of light with a frequency of 4.57 times 10^14 Hz
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1/wavelength = R(1/n1^2 - 1/n2^2)
The n is squared, not the 1 and 2.
n1 will be 2 so the first part is 1/2^2.
Change frequency to wavelength with
c = freq x wavelength.
R is Rydberg constant = 1.097 x 10^7 m
To determine the end value of n in a hydrogen atom transition, we can use the equation:
ΔE = E_final - E_initial
where ΔE is the change in energy, E_final is the final energy level, and E_initial is the initial energy level.
The energy change (ΔE) can be calculated using the equation:
ΔE = h * ν
where h is the Planck's constant (h = 6.626 x 10^-34 J·s) and ν is the frequency of the absorbed photon.
Given the frequency of the absorbed photon is 4.57 × 10^14 Hz, we can calculate ΔE as follows:
ΔE = (6.626 x 10^-34 J·s) * (4.57 × 10^14 Hz)
≈ 3.02 × 10^-19 J
The energy change (ΔE) corresponds to the difference in energy between two energy levels. In the case of a hydrogen atom, this energy change is given by the Rydberg formula:
ΔE = 13.6 eV * (1/n_final^2 - 1/n_initial^2)
We can rearrange this equation to solve for the final energy level (n_final):
1/n_final^2 = 1/n_initial^2 - ΔE / (13.6 eV)
Since the electron starts in n = 2 (n_initial = 2), we can substitute the known values into the equation:
1/n_final^2 = 1/2^2 - (3.02 × 10^-19 J) / (13.6 eV)
1/n_final^2 = 1/4 - (3.02 × 10^-19 J) / (13.6 * 1.602 x 10^-19 J/eV)
= 0.25 - 0.176
1/n_final^2 ≈ 0.074
Taking the square root of both sides:
1/n_final ≈ √0.074
n_final ≈ 1 / √0.074
n_final ≈ 9
Therefore, the end value of n in the hydrogen atom transition is n = 9.
To determine the end value of n in a hydrogen atom transition, we can use the formula:
ΔE = h * ν
where ΔE is the change in energy, h is Planck's constant (6.63 x 10^-34 J·s), and ν is the frequency of the absorbed photon.
In the case of a hydrogen atom transition, the change in energy (ΔE) is given by:
ΔE = E_final - E_initial
where E_final is the energy level of the final state of the electron, and E_initial is the energy level of the initial state.
We can use the formula for the energy levels of the hydrogen atom:
E = -13.6 eV / n^2
where E is the energy level in electron volts (eV), and n is the principal quantum number.
First, let's find the initial energy level (E_initial) when the electron starts in n=2:
E_initial = -13.6 eV / (2^2) = -13.6 eV / 4 = -3.4 eV
Next, we can calculate the change in energy (ΔE) by multiplying the frequency of the absorbed photon (ν) by Planck's constant (h):
ΔE = (6.63 x 10^-34 J·s) * (4.57 x 10^14 Hz)
Now, we can calculate the final energy (E_final) by adding the change in energy (ΔE) to the initial energy level (E_initial):
E_final = E_initial + ΔE
Finally, we can determine the final principal quantum number (n) by rearranging the formula for energy levels and solving for n:
E_final = -13.6 eV / n^2
n^2 = -13.6 eV / E_final
n = √(-13.6 eV / E_final)
Evalute the final equation to find the end value of n.