A laser produced a light of wavelenth 575 nm. How many photons of this light would have to strike a material for the material to absorb 55.1 kJ?
To solve this problem, we need to use the relationship between energy, photons, and wavelength. We can start by finding the energy associated with a single photon using the formula:
E = hc/λ
Where:
E is the energy of a photon
h is Planck's constant (6.626 x 10^-34 J·s)
c is the speed of light (3.00 x 10^8 m/s)
λ is the wavelength of light
Given that the wavelength of light is 575 nm (or 575 x 10^-9 m), we can substitute the values into the formula:
E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/(575 x 10^-9 m)
Calculating this gives us the value of E as approximately 3.451 x 10^-19 J (joules).
Now, we can calculate the number of photons required to provide 55.1 kJ (kilojoules) of energy. We need to convert the kJ value to joules by multiplying it by 1000:
55.1 kJ = 55.1 x 1000 J = 55,100 J
To find the number of photons, we divide the total energy required by the energy of a single photon:
Number of photons = Total energy / Energy per photon
= 55,100 J / 3.451 x 10^-19 J
Evaluating this expression gives us the number of photons needed to deliver 55.1 kJ of energy.