To tackle your question about the sodium lamp, we need to break it down into two parts: first, calculating the energy per photon, and then determining the rate at which these photons are delivered to the sphere. Let's dive into each part step by step.
Calculating Energy per Photon
The energy of a single photon can be calculated using the formula:
E = \frac{hc}{\lambda}
Where:
- E is the energy of the photon.
- h is Planck's constant, approximately 6.626 x 10^{-34} J·s.
- c is the speed of light, about 3.00 x 10^{8} m/s.
- λ is the wavelength of the light, which is given as 589 nm (or 589 x 10^{-9} m).
Now, substituting the values into the formula:
E = \frac{(6.626 x 10^{-34} J·s)(3.00 x 10^{8} m/s)}{589 x 10^{-9} m}
Calculating this gives:
E ≈ 3.37 x 10^{-19} J
Determining the Rate of Photon Delivery
Next, we need to find out how many photons are emitted per second by the lamp. Since the lamp has a power of 100W, we know that it radiates 100 joules of energy per second. To find the number of photons emitted per second, we can use the formula:
Number of photons per second = \frac{Power}{Energy per photon}
Substituting the values we have:
Number of photons per second = \frac{100 J/s}{3.37 x 10^{-19} J}
Calculating this gives:
Number of photons per second ≈ 2.97 x 10^{20} photons/s
Summary of Results
In summary, we found that:
- The energy per photon associated with the sodium light is approximately 3.37 x 10^{-19} J.
- The rate at which photons are delivered to the sphere is about 2.97 x 10^{20} photons/s.
This analysis illustrates how we can use fundamental physics principles to understand the behavior of light and energy in practical scenarios. If you have any further questions or need clarification on any part, feel free to ask!
