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?
(a) frequency = c/(wavelength)
(b) 75 W/(h*f)
where f it the frequency and h is Plank's constant.
(c) certainly not. Frequency does not depend upon brightness. Photons per second does.
By the way, your "posted by" name is an incorrect statement, which disagrees with the facts and the question itself. What is that all about?
(a) To calculate the frequency of the emitted visible light, we can use the equation:
c = λν
where c is the speed of light, λ is the wavelength, and ν is the frequency. We know the wavelength (600 nm), so we need to find the frequency.
First, we need to convert the wavelength from nanometers to meters:
λ = 600 nm = 600 × 10^(-9) m
Now, we can rearrange the equation to solve for the frequency:
ν = c / λ
Plugging in the values:
ν = (3 × 10^8 m/s) / (600 × 10^(-9) m)
Simplifying:
ν ≈ 5 × 10^14 Hz
Therefore, the frequency of the emitted visible light is approximately 5 × 10^14 Hz.
(b) To calculate the number of photons per second of visible light that the source emits, we can use the formula:
E = hf
where E is the energy of a photon, h is Planck's constant (6.63 × 10^(-34) J·s), and f is the frequency of the light.
The energy consumed by the light source is given as 75 W. Since only 5% of this energy is emitted as visible light, we can calculate the energy of the emitted light:
Energy emitted = 0.05 * 75 W
Now, we can use the energy of a photon formula to calculate the number of photons:
Number of photons emitted per second = (Energy emitted) / E
First, we need to calculate the energy of a photon:
E = hf
We can rearrange this equation to solve for f:
f = E / h
Substituting the value of E, we get:
f = (0.05 * 75 W) / (6.63 × 10^(-34) J·s)
Simplifying:
f ≈ 5.66 × 10^14 Hz
Now, we can calculate the number of photons emitted per second:
Number of photons emitted per second = (0.05 * 75 W) / (6.63 × 10^(-34) J·s)
Calculating:
Number of photons emitted per second ≈ 5.66 × 10^14 Hz
Therefore, the source emits approximately 5.66 × 10^14 photons per second of visible light.
(c) No, the frequency of light is not the same thing as the number of photons emitted per second. Frequency refers to the number of oscillations (or cycles) of the light wave that occur per second. On the other hand, the number of photons emitted per second refers to the number of individual light particles (photons) that are emitted per second. Frequency measures the rate at which the oscillations occur, while the number of photons per second measures the rate at which photons are emitted.
(a) To calculate the frequency of the emitted visible light, we can use the formula:
c = λν
where c is the speed of light, λ is the wavelength, and ν is the frequency.
From the given information, the wavelength (λ) of the emitted visible light is 600 nm (or 600 x 10^-9 m).
We know that the speed of light (c) is approximately 3 x 10^8 m/s.
Plugging these values into the formula, we can solve for the frequency (ν):
ν = c / λ = (3 x 10^8 m/s) / (600 x 10^-9 m)
ν ≈ 5 x 10^14 Hz
Therefore, the frequency of the emitted visible light is approximately 5 x 10^14 Hz.
(b) To calculate the number of photons per second of visible light emitted by the source, we can use the formula:
E = hν
where E is the energy of a photon, h is Planck's constant, and ν is the frequency.
Planck's constant (h) is approximately 6.626 x 10^-34 J·s.
Since the energy emitted by the light source is given as 75 W, we can calculate the energy per photon (E) as:
E = (75 W) x (0.05) / Number of photons emitted per second
To solve for the number of photons emitted per second, rearrange the equation:
Number of photons emitted per second = (75 W) x (0.05) / E
Plugging in the values, we get:
Number of photons emitted per second = (75 W) x (0.05) / (6.626 x 10^-34 J·s x 5 x 10^14 Hz)
Calculating this expression will give you the number of photons per second emitted by the source.
(c) No, the frequency of light is not the same thing as the number of photons emitted per second. Frequency is a property of light waves, representing the number of cycles or oscillations of the wave that occur in one second. On the other hand, the number of photons emitted per second represents the quantity of individual photons emitted by a light source over time. While both are related to the energy carried by light, they are distinct properties.