Solving Rydberg's Equation for an Unexcited Hydrogen Atom

[scorpa]

Hello everyone,

I am doing some physics questions with Rydberg's equation and am having some trouble.

An unexcited hydrogen atom (election in the ground state) absorbed a photon of light that had a frequency of 3.09 x 10^15 Hz. Through what transition did the election in this atom undergo?

What I did so far was convert the frequency into wavelength with was 9.7 x 10^-8m. and I know Rydberg's constant is 1.10 x 10^7, but I end up with two variables n variables. I am not quite sure where to go with this unfortunately.

Oh and does it make a difference in your answer whether the hydrogen atom is excited or unexcited?

Thanks in advance for the help!

 

[quasar987]

I don't think this is a Rydberg problem. The electron's energy in the ground state is -13.6 eV, and the frequency of a photon is related to the energy it carries through

$$E=hf$$

where h is Planck's konstant. If you are told that the photon is completely absorbed by the elektron, then according to the principle of conservation of energy, it means that the electron's has absorbed all of the photon's energy. You need to find the elektron's new energy and what state (n=?) does that corespond to?

 

[thepatientmental]

Hello there,

Solving Rydberg's equation for an unexcited hydrogen atom can be a tricky task, but let's break it down step by step. First, let's start with the equation itself:

1/λ = R(1/n1^2 - 1/n2^2)

Where λ is the wavelength of the absorbed light, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

Since we are dealing with an unexcited hydrogen atom, we know that the electron is in the ground state, which has an energy level of n1 = 1. We are also given the frequency of the absorbed light, which we can use to calculate the wavelength as you did. Now, we just need to plug in our values and solve for n2:

1/9.7 x 10^-8m = 1.10 x 10^7(1/1^2 - 1/n2^2)

Solving for n2, we get 3. So, the electron in the hydrogen atom underwent a transition from the ground state (n1 = 1) to the n2 = 3 energy level.

To answer your question about whether it makes a difference if the hydrogen atom is excited or unexcited, the answer is yes. If the atom is already excited, it means that the electron is not in the ground state and therefore, the initial energy level (n1) would be different. This would result in a different final energy level (n2) and thus, a different transition.

I hope this helps clarify things for you. Keep practicing and you'll become a pro at solving Rydberg's equation in no time! Best of luck.