Final answer:
The frequency of light associated with a transition from n=6 to n=3 in a hydrogen atom can be calculated using the Rydberg formula to find the energy of the emitted photon and then applying the relationship E=hf with Planck's constant to find the frequency.
Step-by-step explanation:
Calculating the Frequency of Light in a Hydrogen Atom Transition
To calculate the frequency of light associated with the transition from n=6 to n=3 in a hydrogen atom, we utilize the Rydberg formula for the energy transition in a hydrogen atom:
E = -R_H (1/n^2_1 - 1/n^2_2)
Where E is the energy of the photon emitted, R_H is the Rydberg constant (approximately 1.097 x 10^7 m^-1), and n_1 and n_2 are the principal quantum numbers of the initial and final energy levels, respectively. In this case, n_1 is 6, and n_2 is 3. With this formula, we find the energy E of the emitted photon when the electron falls from the sixth to the third energy level in a hydrogen atom.
Next, we use the relationship E = hf, where h is Planck's constant, approximately 6.626 x 10^-34 J s, and f is the frequency of the emitted light to solve for the frequency.
Breaking it down step by step:
- Calculate the energy difference using the Rydberg formula.
- Use the energy and Planck's constant to solve for the frequency.
Carrying out these calculations will provide the frequency of the light emitted during this specific transition in a hydrogen atom.