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Explanation / Answer

Using, c = f x w

f = frequency

Where, w = wavelength = 150 x 10^-9m = 150nm
c = speed of light = 3 x 10^8m/s

Putting the respective values, we get

3 x 10^8m/s = f * 150 x 10^-9m
f = 2 x 10^15Hz

Now that you know frequency, you can find energy for one Carbon atom:
E = hf

Where, h = planck's constant = 6.626 x10^-34 J*s

E = energy

Putting the respective values, we get

E = 6.626 x10^-34 J*s * 2 x 10^15Hz
E = 1.325 x 10^-18 J

Now that you have the energy per carbon atom, and you are given the total energy, you can find the number of carbon atoms needed:
N = Et / E

Where, Et = Total energy = 5.67 x 10^5J

N = number of carbon atoms

Putting the respective values, we get
N = 5.67 x 10^5J / 1.325 x 10^-18J
N = 4.27 x 10^23 carbon atoms

Thus, the answer is 4.27 x 10^23 carbon atoms.

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