Calculate the energy in radiation of wavelength 550 nm carried by 1) one photon 2) 1 mol of photons
E = hc/wavelength for 1 photon.
That x Avogadro's number for a mole of photons.
To calculate the energy in radiation, we can use the formula:
E = hc/λ
where
E is the energy of the radiation,
h is the Planck's constant (6.626 × 10^-34 J s),
c is the speed of light (3.00 × 10^8 m/s),
and λ is the wavelength of radiation.
1) Energy carried by one photon with a wavelength of 550 nm:
First, we need to convert the wavelength from nm to meters.
1 nm = 1 × 10^-9 m
So, the wavelength in meters is:
550 nm = 550 × 10^-9 m = 5.5 × 10^-7 m
Now we can calculate the energy using the formula:
E = hc/λ
E = (6.626 × 10^-34 J s)(3.00 × 10^8 m/s)/(5.5 × 10^-7 m)
E ≈ 3.62 × 10^-19 J
Therefore, the energy carried by one photon with a wavelength of 550 nm is approximately 3.62 × 10^-19 Joules.
2) Energy carried by 1 mol of photons with a wavelength of 550 nm:
Avogadro's number, N_A = 6.022 × 10^23 mol^-1
To calculate the energy, we need to multiply the energy of one photon by the number of photons in 1 mol.
Number of photons in 1 mol = N_A
E_total = E_photon × N_A
E_total = (3.62 × 10^-19 J) × (6.022 × 10^23 mol^-1)
E_total ≈ 2.18 × 10^5 J
Therefore, the energy carried by 1 mol of photons with a wavelength of 550 nm is approximately 2.18 × 10^5 Joules.
To calculate the energy carried by radiation, we can use the equation:
E = hc/λ
Where:
E is the energy of the radiation,
h is the Planck's constant (approximately 6.626 × 10^-34 J·s),
c is the speed of light (approximately 3.00 × 10^8 m/s), and
λ (lambda) is the wavelength of the radiation.
Let's calculate the energy in radiation of wavelength 550 nm carried by one photon first:
1) One Photon:
λ = 550 nm = 550 × 10^-9 m
E = (6.626 × 10^-34 J·s × 3.00 × 10^8 m/s) / (550 × 10^-9 m)
E ≈ 3.62 × 10^-19 J
Therefore, the energy of radiation carried by one photon with a wavelength of 550 nm is approximately 3.62 × 10^-19 J.
Now, let's calculate the energy in radiation of wavelength 550 nm carried by one mole (6.022 × 10^23) of photons:
2) One Mole of Photons:
To calculate the energy for one mole of photons, we need to multiply the energy per photon by Avogadro's number (6.022 × 10^23), which gives us the total energy.
Energy for one photon = 3.62 × 10^-19 J
Number of photons in one mole = 6.022 × 10^23
E = (3.62 × 10^-19 J) × (6.022 × 10^23)
E ≈ 2.18 × 10^5 J
Therefore, the energy of radiation carried by one mole of photons with a wavelength of 550 nm is approximately 2.18 × 10^5 J.