An electron transition in a single H-atom from n=3 to n=2 results in the release of a single photon. What is the wavelength of this photon in nanometers?
How do I solve this?
1/wavelength = R(1/4 - 1/9)
R = 1.0973732E7
The 1/4 is 1/2^2
The 1/9 is 1/3^2
I tried that but my answer is 6.56*10^(-7) and when I plug it in the site tells me my answer is wrong what went wrong?
The formula I gave you gives wavelength in meters. The question asks for nanometers. Make the conversion. 1 m = 10^9 nm.
Thanksss!!! :D it worked much appreciated!
To solve this question, you need to use the equation for the energy of a photon:
E = hc/λ
Where:
E is the energy of the photon
h is the Planck's constant (6.62607015 × 10^-34 J·s)
c is the speed of light (2.998 × 10^8 m/s)
λ is the wavelength of the photon
First, let's find the energy difference between the two energy levels (n=3 and n=2) using the formula:
ΔE = E(final) - E(initial) = -R_H*(1/n(final)^2 - 1/n(initial)^2)
Where:
R_H is the Rydberg constant for hydrogen (approximately 2.18 × 10^-18 J)
n(final) is the final energy level (in this case, n=2)
n(initial) is the initial energy level (in this case, n=3)
Plugging in the values:
ΔE = -R_H*(1/2^2 - 1/3^2)
Now, calculate the value of ΔE.
Next, use the energy-wavelength relationship to find the wavelength of the photon. Rearranging the equation, we have:
λ = hc / ΔE
Plug in the values for h, c, and ΔE, and calculate the wavelength.
Lastly, convert the wavelength from meters to nanometers by multiplying by 10^9.
Following these steps, you should be able to find the wavelength of the photon in nanometers.