15 At a particular location and time, sunlight is measured on a 1 m2 solar collector with an
intensity of 500.0 W. If the peak intensity of this sunlight has a wavelength of 5.60 x 10-7 m,
(a) What is the frequency of this light? When you input large numbers such as those in this
problem, then input the numbers with parenthesis so as to obtain the correct answer. (b)
What is the energy of one photon of this light? (c) How many photons are arriving each
second? When you input large numbers such as those in this problem, then input the
numbers with parenthesis so as to obtain the correct answer.
(a) frequency = (3*10^8 m/s)/(5.60*10^-7m) = ____ Hz
(b) E = h*(frequency) = ___ J
where h is Planck's constant.
(c) Photon arrival rate =
500 Watts/E(Joules per photon)
= _____ photons/sec
I don't get the significance of putting large numbers in parentheses. It does not make the calculation more accurate. Just use scientific notation.
fbaba
c) 1.14 x 10^21 photons
(a) Well, if the wavelength of the light is given as 5.60 x 10^-7 m, we can use the speed of light equation to find the frequency. Let me grab my calculator. *beep boop beep boop* Ah, the speed of light (c) is approximately 3 x 10^8 m/s. So, the frequency (f) is equal to the speed of light divided by the wavelength (λ). Let's crunch those numbers.
f = (3 x 10^8 m/s) / (5.60 x 10^-7 m) ≈ 5.357 x 10^14 Hz
(b) To find the energy of one photon, we can use the equation E = hf, where h is the Planck's constant (approximately 6.63 x 10^-34 J·s). Let's plug in the frequency we just calculated.
E = (6.63 x 10^-34 J·s) × (5.357 x 10^14 Hz) ≈ 3.55 x 10^-19 J
(c) Now, to find the number of photons arriving each second, we can use the power (P) and energy per photon (E) relationship. Power is energy per second, so we divide the power by the energy of one photon.
Number of photons = Power / Energy per photon
Number of photons = 500.0 W / 3.55 x 10^-19 J
And I must inform you that the result for this calculation is an extremely large number. Be prepared to be amazed...
Number of photons ≈ 1.41 x 10^21 photons per second
That's a boatload of photons! I hope your solar collector is ready for the party!
(a) To calculate the frequency of light, you can use the equation:
frequency = speed of light / wavelength
The speed of light is a constant value, approximately 3.00 x 10^8 m/s.
Given that the wavelength is 5.60 x 10^-7 m, we can substitute these values into the equation:
frequency = (3.00 x 10^8 m/s) / (5.60 x 10^-7 m)
Simplifying this equation gives us:
frequency = (3.00 x 10^8 m/s) * (1 / (5.60 x 10^-7 m))
Now, multiply and divide the numbers:
frequency = (3.00 x 10^8 m/s) * (1 / (5.60 x 10^-7 m))
≈ (3.00 x 10^8 m/s) * (1.79 x 10^6 m)
≈ 5.37 x 10^14 Hz (rounded to two significant figures)
Therefore, the frequency of this light is approximately 5.37 x 10^14 Hz.
(b) The energy of one photon can be calculated using Planck's equation:
energy of a photon = Planck's constant * frequency
The Planck's constant is approximately 6.63 x 10^-34 J·s.
Substituting the frequency we calculated in part (a) into the equation:
energy of a photon = (6.63 x 10^-34 J·s) * (5.37 x 10^14 Hz)
Now, multiply these values:
energy of a photon ≈ (6.63 x 10^-34 J·s) * (5.37 x 10^14 Hz)
≈ 3.56 x 10^-19 J (rounded to two significant figures)
Therefore, the energy of one photon of this light is approximately 3.56 x 10^-19 J.
(c) To calculate the number of photons arriving each second, we can use the intensity of the sunlight measured on the solar collector.
Intensity is defined as power per unit area. So, the power of light arriving on the solar collector can be calculated by multiplying the intensity by the area:
power = intensity * area
Given that the intensity is 500.0 W and area is 1 m^2, we can substitute these values into the equation:
power = 500.0 W * 1 m^2
= 500.0 W
Now, to calculate the number of photons arriving each second, we can divide the power by the energy of one photon:
number of photons per second = power / energy of one photon
Substituting the power and energy values we calculated:
number of photons per second = 500.0 W / (3.56 x 10^-19 J)
Now, divide these values:
number of photons per second ≈ 500.0 W / (3.56 x 10^-19 J)
≈ 1.40 x 10^21 photons/s (rounded to two significant figures)
Therefore, approximately 1.40 x 10^21 photons are arriving each second.