Final answer:
The energy of the photon emitted by the harmonic oscillator when it drops from energy level 8 to energy level 3 is approximately 1.30 × 10^10 Hz.
Step-by-step explanation:
To calculate the energy of the emitted photon, we can use the equation:E = hf
where:
- E is the energy of the photon
- h is Planck's constant (6.626 × 10-34 J·s)
- f is the frequency of the photon
In this case, we need to find the frequency of the emitted photon when an oscillator drops from energy level 8 to energy level 3. Since the energy levels of a harmonic oscillator are quantized, we can assume that the energy difference between each level is the same. So, we can find the frequency using the formula:f = ΔE / h
where ΔE is the energy difference between the two levels.
First, let's calculate the energy difference between energy level 8 and energy level 3:ΔE = E8 - E3
Substituting the given values into the equation:ΔE = (8.6 × 10-24 J) - (2.3 × 10-2 m) = 8.598 × 10-24 J
Now, let's calculate the frequency:f = ΔE / h = (8.598 × 10-24 J) / (6.626 × 10-34 J·s) ≈ 1.30 × 1010 Hz
So, the energy of the photon emitted by the harmonic oscillator when it drops from energy level 8 to energy level 3 is approximately 1.30 × 1010 Hz.