How many photons of visible light result if a 60-keV x-ray photon is converted into green visible light with 10% efficiency?
To determine the number of photons of visible light resulting from the conversion of a 60-keV x-ray photon into green visible light with 10% efficiency, we can use the following steps:
Step 1: Calculate the energy of a single green photon
The energy of a single photon can be determined using the equation E = hf, where E is the energy, h is Planck's constant (6.62607015 x 10^-34 J·s), and f is the frequency.
Green light is typically in the range of 495 to 570 nanometers (nm) on the electromagnetic spectrum. Let's assume a wavelength of 550 nm for green light.
To find the frequency, we can use the equation f = c/λ, where c is the speed of light (3.00 x 10^8 m/s) and λ is the wavelength.
f = (3.00 x 10^8 m/s) / (550 x 10^-9 m)
f ≈ 5.45 x 10^14 Hz
Now, we can calculate the energy of a single green photon:
E = (6.62607015 x 10^-34 J·s) * (5.45 x 10^14 Hz)
E ≈ 3.60 x 10^-19 J
Step 2: Calculate the number of green photons produced
To determine the number of green photons produced, we need to know the energy conversion efficiency, which is given as 10%.
The efficiency indicates the proportion of the energy of the x-ray photon that is converted into visible light. In this case, since the efficiency is 10%, only 10% of the energy of the x-ray photon will be converted.
Let's find the energy converted from the x-ray photon:
Energy converted = 10% of (60 keV)
Converting keV to joules:
1 keV = 1.60218 x 10^-16 J
Energy converted = 10% of (60 x 1.60218 x 10^-16 J)
Energy converted ≈ 9.61 x 10^-17 J
Now, we can calculate the number of green photons produced:
Number of photons = Energy converted / Energy of a single green photon
Number of photons = (9.61 x 10^-17 J) / (3.60 x 10^-19 J)
Number of photons ≈ 267 photons
Therefore, approximately 267 photons of visible green light will result if a 60-keV x-ray photon is converted into green visible light with 10% efficiency.