A 75 W light source consumes 75 W of electric power. Typically only about 5% of this energy is emitted as visible light of wavelength 600 nm. (a) Calculate the frequency of the emitted visible light. (b) How many photons per second of visible light does the source emit? (c) Is the frequency of light the same thing as as the number of photons emitted per second?
HELP please!
What is your question? I will be happy to critique your thinking or work, but not so happy to do it for you.
I don't know how to get the frequency, I think if I can figure that out I could get the rest, but I am not sure where the two 75 W come in and the 5% like where am I suppose to put them in any equation?
You get the frequency from the wavelength.
To answer these questions, we need to understand the relationship between energy, power, wavelength, frequency, and the concept of photons.
(a) To calculate the frequency of the emitted visible light, we can use the equation:
c = λν
Where:
c is the speed of light (approximately 3.00 × 10^8 meters per second),
λ is the wavelength of light (600 nm, which is equivalent to 600 × 10^(-9) meters), and
ν is the frequency of light (which we need to find).
Rearranging the equation, we get:
ν = c / λ
Substituting the values, we have:
ν = (3.00 × 10^8 m/s) / (600 × 10^(-9) m)
ν = 5.00 × 10^14 Hz
So, the frequency of the emitted visible light is approximately 5.00 × 10^14 Hz.
(b) To find the number of photons per second of visible light emitted by the source, we need to use another equation related to energy and photons:
E = hν
Where:
E is the energy of one photon (which we need to find),
h is Planck's constant (approximately 6.63 × 10^(-34) J·s), and
ν is the frequency of light.
Rearranging the equation, we get:
E = hν / 1
Since we know the power consumed by the light source is 75 W, we can use the equation:
Power = Energy / Time
Energy = Power × Time
Let's consider Time as 1 second:
Energy = 75 J
Now, substituting the values into the equation:
75 J = (6.63 × 10^(-34) J·s) × (5.00 × 10^14 Hz)
75 J = 3.31 × 10^(-19) J
Therefore, the energy of one photon is approximately 3.31 × 10^(-19) J.
Since the energy of one photon is needed to calculate the number of photons, we can divide the total energy (75 J) by the energy of one photon:
Number of photons = Total energy / Energy of one photon
Number of photons = 75 J / (3.31 × 10^(-19) J)
Calculating this value gives us:
Number of photons ≈ 2.27 × 10^20 photons
So, the light source emits approximately 2.27 × 10^20 photons per second.
(c) The frequency of light and the number of photons emitted per second are related but not the same thing. Frequency refers to the number of wave cycles passing a point per second, while the number of photons emitted per second represents the quantized particles of light. One way to think about it is that the frequency determines the color or wavelength of light, while the number of photons determines the intensity or brightness of the light.