Question:- How many photons are contained in a flash of green light that contains 189 kJ of energy?
Answer
In solving this problem the following steps are followed; the first one is that of establishing the wavelength of green light and having a formula by which the energy of photon relates with its wavelength.
The often-used characteristic wavelength of green light is approximately 550 $nm$. The energy of a photon is given by the formula: This makes A = hc/λ, Where h = Planck’s constant=6.63 * 10^-34 Js., the velocity of light c = 3 * 10^8 ms and λ is the wavelength of light emitted.
Substituting the obtained values, we have the energy of single green photon E = (6.63* 10^-34 J·s) (3* 10^8 m/s) / 550 *10^-9 m ≈ 3. 62 * 10^-19 J.
To find the number of photons in 189 kJ, we divide the total energy by the energy of a single photon: 189 * 10(3) J/ (3.62 × 10^-19 J/photon) ≈ 5.22 × 10^21 photons.
Thus, as per the analysis carried out above, the aforesaid number of green lights makes the energy amount equal to 189 kJ, or 5. 22 * 10^21 photons.