The energy of a single photon can be calculated using two different versions of the equation, depending on whether you are using the wavelength or frequency of the light:
Using the equation involving wavelength (λ): Energy (E) = (Planck's constant (h) × speed of light (c)) / wavelength (λ)
Using the equation involving frequency (ν): Energy (E) = Planck's constant (h) × frequency (ν)
Now, let's calculate the energy of a single photon with a wavelength of 532 nm.
Using the equation involving wavelength: Given: Wavelength (λ) = 532 nm = 532 × 10^(-9) m (since 1 nm = 10^(-9) m) Planck's constant (h) = 6.62607015 × 10^(-34) J·s (exact value) Speed of light (c) = 2.99792458 × 10^8 m/s (approximate value)
Plugging in these values into the equation: Energy (E) = (6.62607015 × 10^(-34) J·s × 2.99792458 × 10^8 m/s) / (532 × 10^(-9) m) = 3.73718994 × 10^(-19) J ≈ 3.74 × 10^(-19) J
Therefore, the energy of a single photon with a wavelength of 532 nm is approximately 3.74 × 10^(-19) J.
To calculate the energy for 1 mol of those photons, we need to know the Avogadro's number (N_A) as well. Avogadro's number is approximately 6.02214076 × 10^23 mol^(-1) (exact value).
Given: Number of photons in 1 mol = Avogadro's number (N_A) = 6.02214076 × 10^23 mol^(-1)
Energy for 1 mol of photons = Energy of a single photon × Number of photons in 1 mol = (3.74 × 10^(-19) J) × (6.02214076 × 10^23 mol^(-1)) = 2.25299144 J
Therefore, the energy for 1 mol of photons with a wavelength of 532 nm is approximately 2.253 J.