Calculate the energy in joules per photon of red light having a wavelength 655 nm. What is the energy of 1 mol of these photons?
E = hc/wavelength. This gives you the energy of 1 photon (in joules). For a mole, multiply by 6.022E23. Don't forget that the wavelength must be in meters.
To calculate the energy in joules per photon of red light with a wavelength of 655 nm, we can use the formula:
E = (hc) / λ
where:
E is the energy of a photon
h is Planck's constant (6.626 × 10^(-34) J·s)
c is the speed of light (2.998 × 10^8 m/s)
λ is the wavelength in meters
Step 1: Convert the wavelength to meters
Given that the wavelength is 655 nm, we need to convert it to meters. We know that 1 nm = 1 × 10^(-9) m.
Therefore, the wavelength in meters (λ) is:
λ = 655 nm * (1 × 10^(-9) m/1 nm) = 6.55 × 10^(-7) m
Step 2: Calculate the energy of a photon
Using the formula E = (hc) / λ, we can now calculate the energy of a single photon:
E = (6.626 × 10^(-34) J·s * 2.998 × 10^8 m/s) / (6.55 × 10^(-7) m)
E ≈ 3.03 × 10^(-19) J
Therefore, the energy in joules per photon of red light with a wavelength of 655 nm is approximately 3.03 × 10^(-19) J.
Step 3: Calculate the energy of 1 mol of these photons
To find the energy of 1 mol of these photons, we need to multiply the energy per photon by Avogadro's number, which is approximately 6.022 × 10^23 mol^(-1).
Energy of 1 mol of photons = (3.03 × 10^(-19) J/photon) * (6.022 × 10^23 mol^(-1))
Energy of 1 mol of photons ≈ 1.83 × 10^5 J/mol
Therefore, the energy of 1 mol of these photons is approximately 1.83 × 10^5 J/mol.
To calculate the energy per photon, we can use the formula:
E = hc / λ
where E is the energy per photon, h is the Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength of the light in meters.
First, let's convert the wavelength of the red light from nanometers (nm) to meters (m). We know that 1 nm is equal to 10^-9 m. Therefore:
655 nm = 655 × 10^-9 m = 6.55 × 10^-7 m
Now, let's substitute the values into the equation:
E = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (6.55 × 10^-7 m)
The units cancel out, giving us energy in joules per photon.
E ≈ 3.02 × 10^-19 J
So, the energy per photon of red light with a wavelength of 655 nm is approximately 3.02 × 10^-19 J.
To calculate the energy of 1 mole of these photons, we need to multiply the energy per photon by Avogadro's number (6.022 × 10^23 mol^-1). This converts the energy to joules per mole.
Energy of 1 mol of photons = (3.02 × 10^-19 J) × (6.022 × 10^23 mol^-1)
Calculating this:
Energy of 1 mol of photons ≈ 1.82 × 10^5 J/mol
Therefore, the energy of 1 mol of red light photons with a wavelength of 655 nm is approximately 1.82 × 10^5 J/mol.