To determine the number of photons of light with a wavelength of 4000 picometers (pm) that provide 1 joule (J) of energy, we can use the formula:
E = hf
We can convert the wavelength of the photon to frequency using the formula:
f = c / λ
where:
c = speed of light (299,792,458 m/sec)
λ = wavelength of the photon in meters
Converting the wavelength of the photon to meters:
4000 pm = 4000 x 10^-12 m
Substituting into the frequency formula:
f = c / λ
f = 299,792,458 m/s / (4000 x 10^-12 m)
f = 7.4948 x 10^16 Hz
Now, we can calculate the energy of a single photon using the first formula:
E = hf
E = (6.626 x 10^-34 J s) x (7.4948 x 10^16 Hz)
E = 4.967 x 10^-17 J
To find the no of photons that provide 1 J of energy, we divide the total energy by the energy of a single photon:
Number of photons = 1 J / (4.967 x 10^-17 J/photon)
Number of photons = 2.012 x 10^16 photons
Therefore, approximately 2.012 x 10^16 photons of light with a wavelength of 4000 pm provide 1 J of energy.
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