A 100-watt lightbulb radiates energy at a rate of 100 J/s (The watt, a unit of power, or energy over time, is defined as 1 J/s). If all of the light emitted has a wavelength of 500nm, how many photons are emitted per second? (Assume three significant figures in this calculation.)
E of 1 photon = hc/wavelength
E of 1 photon x # photons = 100 J
2.52*10^-18??? is what I got
never mind it tells me that it is not right. I don't know what I am doing wrong. (6.626*10^-34)(3.00*10^8)/ (500*10^-9)= 3.98*10^-19 so 100/ 3.98*10^-19= 2.52*10^-18
Thanks for showing your work.
I think your error is in the last step. If I divide 100/4E-19 I get an answer like 25E+19 or 2.5E20 Check that out.
To calculate the number of photons emitted per second, we need to use the formula that relates power, energy, and photon energy:
Power = Energy / time
Power = (Number of photons x Energy per photon) / time
We know that the power emitted by the lightbulb is 100 J/s, and the energy per photon can be calculated using the equation:
Energy per photon = Planck's constant x speed of light / wavelength
So, let's calculate the energy per photon:
Plank's constant (h) = 6.626 x 10^-34 J·s
Speed of light (c) = 3.00 x 10^8 m/s
Wavelength (λ) = 500 nm = 500 x 10^-9 m
Energy per photon = (6.626 x 10^-34 J·s x 3.00 x 10^8 m/s) / (500 x 10^-9 m)
Now, let's compute the value:
Energy per photon = 3.9768 x 10^-19 J
Now, we can substitute the values back into the power equation to find the number of photons emitted per second:
Power = (Number of photons x Energy per photon) / time
100 J/s = (Number of photons x 3.9768 x 10^-19 J) / 1 s
To solve for the number of photons, we rearrange the equation:
Number of photons = (Power x time) / Energy per photon
Number of photons = (100 J/s x 1 s) / 3.9768 x 10^-19 J
Finally, we can calculate the number of photons emitted per second:
Number of photons = 2.5166 x 10^20 photons/s
Therefore, approximately 2.517 x 10^20 photons are emitted per second.