The watt is the derived SI unit of power, the measure of energy per unit time: 1 W = 1 J/s. A semiconductor laser in a CD player has an output wavelength of 780 nm and a power level of 0.10 mW. How many photons strike the CD surface during the playing of a CD 38 minutes in length?
The energy of each photon is
E = hc/wavelength
E = 6.626E-34 x 3E8
780E-9 = approx 3E-19 (but you need to do this and all of the other calculations better than I'm estimating).
How many seconds do we have?
Thats 38 min x (60 s/min) = about 2300 s.
power is 0.1mW = 0.0001 W = J/s
0.0001*2300s = about 0.23 J
3E-19 J/photon x #photons = 0.23 J
Solve for #photons.
Check my thinking.
To find the number of photons that strike the CD surface during the playing of a CD, we need to calculate the total energy emitted by the semiconductor laser and then convert it to the number of photons.
Step 1: Convert the power level of the laser to watts.
Given power level = 0.10 mW
1 milliwatt (mW) = 0.001 watts (W)
Convert: 0.10 mW = 0.10 * 0.001 W = 0.0001 W
Step 2: Calculate the energy emitted by the laser per second.
Energy emitted per second (E) = power (P)
E = 0.0001 J/s (From the definition of power, 1 W = 1 J/s)
Step 3: Convert the wavelength to meters.
Given wavelength = 780 nm
1 nanometer (nm) = 1 x 10^-9 meters (m)
Convert: 780 nm = 780 x 10^-9 m = 7.8 x 10^-7 m
Step 4: Calculate the energy per photon.
Energy per photon (Ephoton) = Planck's constant (h) * speed of light (c) / wavelength
Planck's constant (h) = 6.626 x 10^-34 J.s
Speed of light (c) = 3 x 10^8 m/s
Ephoton = (6.626 x 10^-34 J.s * 3 x 10^8 m/s) / (7.8 x 10^-7 m)
Step 5: Calculate the number of photons per second.
Number of photons per second = Energy emitted per second / Energy per photon
Number of photons per second = (0.0001 J/s) / Ephoton
Step 6: Calculate the total number of photons for 38 minutes.
Total number of photons = Number of photons per second * 38 minutes * 60 seconds
You can substitute the values and calculate the final result.
To calculate the number of photons that strike the CD surface during the playing of a CD, we need to follow these steps:
Step 1: Convert the power level from milliwatts (mW) to watts (W).
Given power level = 0.10 mW
To convert milliwatts to watts, divide the power level by 1000:
0.10 mW = 0.10/1000 W = 0.0001 W
Step 2: Calculate the energy per photon using the formula:
Energy (E) = Planck's constant (h) * speed of light (c) / wavelength (λ)
The Planck's constant (h) is approximately 6.626 x 10^-34 J·s.
The speed of light (c) is approximately 3 x 10^8 m/s.
The wavelength (λ) is given as 780 nm, which is equivalent to 780 x 10^-9 m.
Substituting the values into the formula:
E = (6.626 x 10^-34 J·s * 3 x 10^8 m/s)/(780 x 10^-9 m)
E ≈ 2.537 x 10^-19 J
Step 3: Calculate the number of photons using the formula:
Number of photons = Power (P) / Energy per photon (E)
Substituting the values:
Number of photons = 0.0001 W / (2.537 x 10^-19 J)
Number of photons ≈ 3.943 x 10^14 photons
Step 4: Calculate the total number of photons for the CD playing time.
CD playing time = 38 minutes = 38 x 60 seconds
Total number of photons = Number of photons * CD playing time
Total number of photons ≈ (3.943 x 10^14 photons) * (38 x 60 seconds)
Total number of photons ≈ 8.993 x 10^17 photons
Therefore, during the playing of a 38-minute CD, approximately 8.993 x 10^17 photons will strike the CD surface.