To calculate how many photons are in a certain amount of energy (joules) we need to know how much energy is in one photon.
Start by using two equations:
Energy of a photon = Frequency * Planck's constant (6.626 * 10^(-34) J-s)
Speed of light (constant 3 * 10^8 m/s) = Frequency * Wavelength
Which means:
frequency = Speed of Light / Wavelength
So energy of a photon = (Speed of light * Planck's constant)/(Wavelength)
You may have seen this equation as E = hc/<span>λ</span>
We have a wavelength of 691 nm or 691 * 10^-9 meters
So we can plug in all of our knowns:
E = (6.626 * 10^(-34) J-s) * (3.00 * 10^8 m/s) / (691 * 10^-9 m) =
2.88 * 10^(-19) joules per photon
Now we have joules per photon, and the total number of joules (0.862 joules)
,so divide joules by joules per photon, and we have the number of photons:
0.862 J/ (2.88 * 10^(-19) J/photon) = 3.00 * 10^18 photons.
Answer:
4.59 × 10⁻³⁶ kJ/photon
Explanation:
Step 1: Given and required data
- Wavelength of the violet light (λ): 433 nm
- Planck's constant (h): 6.63 × 10⁻³⁴ J.s
- Speed of light (c): 3.00 × 10⁸ m/s
Step 2: Convert "λ" to meters
We will use the conversion factor 1 m = 10⁹ nm.
433 nm × 1 m/10⁹ nm = 4.33 × 10⁷ m
Step 3: Calculate the energy (E) of the photon
We will use the Planck-Einstein's relation.
E = h × c/λ
E = 6.63 × 10⁻³⁴ J.s × (3.00 × 10⁸ m/s)/4.33 × 10⁷ m
E = 4.59 × 10⁻³³ J = 4.59 × 10⁻³⁶ kJ
