Final answer:
The frequency of the light emitted by a hydrogen atom during a transition from the n = 6 to the n = 3 principal energy level is approximately -3.04 x 10^14 Hz.
Step-by-step explanation:
To calculate the frequency of the light emitted by a hydrogen atom during a transition from the n = 6 to the n = 3 principal energy level, we can use the equation:
f = (E2 - E1) / h
Where f is the frequency, E2 is the energy of the initial level (n = 6), E1 is the energy of the final level (n = 3), and h is Planck's constant (6.626 x 10^-34 J∙s).
Plugging in the values, we have:
f = (-3.4 eV - (-1.5 eV)) / (6.626 x 10^-34 J∙s)
Calculating the numerator:
f = -1.9 eV / (6.626 x 10^-34 J∙s)
Converting eV to Joules:
f = -1.9 x 1.6 x 10^-19 J / (6.626 x 10^-34 J∙s)
Further simplifying:
f = -3.04 x 10^14 Hz
Therefore, the frequency of the light emitted by the hydrogen atom during this transition is approximately -3.04 x 10^14 Hz.