A hydrogen atom initially in its ground state (n = 1) absorbs a photon and ends up in the state for which n = 3.
What is the energy of the absorbed photon?
*I found the energy of the atom at the ground state and at n = 3. I subtracted the final from the initial to get a value of 9.1 eV but it wasn't correct. Am I doing this correctly?
No, you are not calculating it correctly. The energy of a photon can be calculated using the formula:
E = ΔE = hf
Where E is the energy of the photon, ΔE is the change in energy of the hydrogen atom, h is Planck's constant (6.626 x 10^-34 J s), and f is the frequency of the photon.
The change in energy of the hydrogen atom can be found using the equation:
ΔE = E(final state) - E(initial state)
The energy of a hydrogen atom in the ground state (n = 1) is given by the Rydberg formula:
E(initial state) = -13.6 eV / n^2
So, substituting n = 1, we get:
E(initial state) = -13.6 eV
The energy of a hydrogen atom in the state where n = 3 can be calculated in the same way:
E(final state) = -13.6 eV / n^2
= -13.6 eV / (3^2)
= -13.6 eV / 9
= -1.511 eV
Now, we can calculate the change in energy:
ΔE = E(final state) - E(initial state)
= -1.511 eV - (-13.6 eV)
= 12.089 eV
So, the energy of the absorbed photon is 12.089 eV.
To find the energy of the absorbed photon, we need to calculate the energy difference between the initial and final states of the hydrogen atom.
The energy levels of a hydrogen atom are given by the formula:
E = -13.6 eV / n^2
where n is the principal quantum number.
In this case, the initial state is n = 1 (ground state) and the final state is n = 3.
To calculate the energy difference, we subtract the energy of the initial state from the energy of the final state:
∆E = E_final - E_initial
∆E = (-13.6 eV / 3^2) - (-13.6 eV / 1^2)
∆E = (-13.6 eV / 9) - (-13.6 eV / 1)
∆E = -1.51 eV - (-13.6 eV)
∆E = 12.09 eV
So the energy of the absorbed photon is 12.09 eV.
It appears you made an error when subtracting the initial energy from the final energy. Make sure to subtract the values correctly and check your calculation.
13.6ev(1/1^2-1/3^2) =13.6ev *9/10
Not your answer.