Calculate thr number of photons having a wavelength of 10.0 μm required to produce 1.0 kJ of energy.
ok so first you need to figure out the energy of ONE photon with that wavelength. Using E=hc/lambda, you get E= 1.99 10^-20 J/photon. Now, how many photons do you need to add up to get to one kilojoule=1000 joules? 1000J / (1.99 10^-20 J/photon) = approximately 5 * 10^22 photons
hope this helps
Answer:
The number of photons are \(5.028\times 10^{27}\).
Explanation:
\(E=\frac{h\times c}{\lambda}\)
where,
E = energy of photon =
h = Planck's constant = \(6.63\times 10^{-34}Js\)
c = speed of light = \(3\times 10^8m/s\)
\(\lambda\) = wavelength = 10.0 μm =\(10^{-5} m\)
1 μm = \(10^{-6} m\)
\(E=\frac{6.63\times 10^{-34}Js\times 3\times 10^8m/s}{10^{-5} m}\)
\(E=1.989\times 10^{-20} Joules\)
Let the n number of photons with energy equal to E' = 1.0 kJ = 1000 J
\(n\times E=E'\)
\(n\times 1.989\times 10^{-20} J=1000 J\)
\(n=\frac{1000 J}{1.989\times 10^{-20} J}=5.028\times 10^{27}\)
The number of photons are \(5.028\times 10^{27}\).