A line in the Lyman series of the hydrogen atom emission results from the transition of an
electron from the n=3 level to the ground state level.
a) What n level (#) is the ground state level for the hydrogen atom?
b) What is the energy of this photon in Joules?
c) What is the frequency (in Hz) and wavelength (in nm) of the emitted photon?
I don't understand this problem at all, I'm very confused, help would be greatly appreciated
a) The ground state level for the hydrogen atom corresponds to n=1. In the Lyman series, the electron transitions from higher energy levels to the ground state level (n=1).
b) To find the energy of the photon emitted during this transition, we can use the formula:
E = (hc) / λ
Where:
E is the energy of the photon
h is Planck's constant (6.62607015 x 10^-34 J s)
c is the speed of light (2.998 x 10^8 m/s)
λ is the wavelength of the photon emitted
For the Lyman series, we know that the transition is from n=3 to n=1. The formula for calculating the wavelength of the emitted photon is given by:
1/λ = R_H (1/n_f^2 - 1/n_i^2)
Where:
R_H is the Rydberg constant (1.097373 x 10^7 m^-1)
n_f is the final energy level (in this case, 1 for the ground state)
n_i is the initial energy level (in this case, 3)
Plugging in the values, we can calculate the wavelength of the emitted photon using the wavelength formula. Then, we can find the energy of the photon using the energy formula.
Let's calculate it step by step:
1. Calculate the wavelength using the Rydberg formula:
1/λ = R_H (1/1^2 - 1/3^2)
Simplifying further:
1/λ = R_H (1 - 1/9)
1/λ = R_H (8/9)
λ = 9/8R_H
2. Calculate the energy using the energy formula:
E = (hc) / λ
E = (6.62607015 x 10^-34 J s) * (2.998 x 10^8 m/s) / (9/8R_H)
Simplifying further:
E = (6.62607015 x 10^-34 J s) * (2.998 x 10^8 m/s) * (8R_H / 9)
E = (6.62607015 x 10^-34 J s) * (2.998 x 10^8 m/s) * (8 * 1.097373 x 10^7 m^-1 / 9)
Calculating the numerical value:
E ≈ 2.1799 × 10^(-18) J
Therefore, the energy of the photon emitted during the transition from the n=3 level to the ground state level is approximately 2.1799 × 10^(-18) Joules.
a) one
b) look it up