If a Li 2+ ion, initially in the 2nd excited state absorbs a photon of light with a fequency of 2.82 X 10^6 GHz, what will be the final energy level for this electron? Show all stepts to get final energy level.
i have no clue what this question is even asking :[?
I thought I answered this but I don't see my post. The trick is to use the Rydberg formula for the energy levels of Li2+. The Rydberg constant is nine times the value for hydrogen. The frequency of the absorbed light tells you the difference of the energy levels. You get the initial energy level by using n=2 in the Rydberg formula, which says that the energy level is -(constant)/n^2
You will find a full explanation at
http://en.wikipedia.org/wiki/Rydberg_formula
No worries! I can help you understand and solve this question step by step.
First, let's break down the information given in the question. We have a Li 2+ ion, which means it has lost two electrons compared to a neutral lithium atom. The "2nd excited state" refers to the energy level of the electron in the atom. By absorbing a photon of light with a frequency of 2.82 X 10^6 GHz, we want to determine the final energy level the electron will occupy.
To solve this question, we need to know the relationship between the energy of a photon and its frequency. The formula for the energy of a photon is given by E = h * ν, where E is the energy, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and ν is the frequency of the light.
Now let's move on to the solution:
Step 1: Convert the given frequency to the corresponding energy using the formula E = h * ν.
E = (6.626 x 10^-34 J·s) * (2.82 x 10^6 GHz)
E = 1.87 x 10^-21 J
Step 2: Determine the energy difference between the initial and final states of the electron.
The energy difference can be calculated by subtracting the energy of the initial state from the energy of the final state.
Step 3: Use the energy difference to determine the final energy level.
The energy levels of an electron in an atom are quantized, meaning they are discrete and can be represented by whole numbers. The energy levels are normally labeled using the principal quantum number, n. The higher the value of n, the higher the energy level.
To determine the final energy level, we need to find the value of n that corresponds to the energy difference calculated in Step 2. This can be done by referring to a table or diagram of energy levels for the specific atom or ion.
The energy levels for Li 2+ can be represented by the formula: E = -13.6 eV / (n^2), where E is the energy in electron volts (eV), and n is the principal quantum number.
Rearrange the formula to solve for n:
n = sqrt(-13.6 eV / E)
Substitute the values to find n:
n = sqrt(-13.6 eV / (1.87 x 10^-21 J))
Step 4: Convert the value of n to the final energy level.
Using the calculated value of n, which should be a whole number, we can determine the final energy level. The energy level corresponding to each value of n can be found in the same table or diagram used in Step 3.
And that's it! By following these steps, you should be able to determine the final energy level for the Li 2+ ion.