Consider a red flame color produced by excited lithium with a wavelength of 671 nm. What is the mass equivalent of 1 mol of photons of this wavelength?
I can get as far as Js of E
Can't seem to find equation to turn Js into mols, or photons into mols, for Js into photons.
I'm lost
E=h*c/lambda Solve for E, the energy in one photon, then multily it by avagradros number.
ahh, of course, thank you.
To solve this problem, we need to apply some basic concepts from physics and chemistry. Let's break it down step by step:
Step 1: Calculate the energy of one photon.
The energy of a photon can be calculated using the equation:
E = hc/λ
where E is the energy of the photon, h is the Planck constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light in meters.
In this case, the wavelength is given as 671 nm, which is equivalent to 671 x 10^-9 m. Plugging these values into the equation, we can find the energy of one photon.
E = (6.626 x 10^-34 J·s) x (3.00 x 10^8 m/s) / (671 x 10^-9 m)
E ≈ 9.931 x 10^-20 J (rounded to three significant figures)
Step 2: Calculate the energy of one mole of photons.
To calculate the energy of one mole of photons, we need to know the Avogadro constant (6.022 x 10^23 mol^-1), which represents the number of particles in one mole.
To find the energy of one mole of photons, we multiply the energy of one photon by the Avogadro constant:
Energy of one mole of photons = Energy of one photon × Avogadro constant
E(mol photons) = E × N_A
(where N_A is the Avogadro constant, approximately 6.022 x 10^23 mol^-1)
E(mol photons) = (9.931 x 10^-20 J) × (6.022 x 10^23 mol^-1)
E(mol photons) ≈ 5.975 x 10^4 J (rounded to three significant figures)
Step 3: Convert energy to mass using Einstein's mass-energy equivalence.
Einstein's formula, E = mc^2, gives us a way to convert energy (E) to mass (m).
To find the mass equivalent of energy, we rearrange the formula to solve for mass:
m = E / c^2
where m is the mass in kilograms, E is the energy in joules, and c is the speed of light (approximately 3.00 x 10^8 m/s).
m = (5.975 x 10^4 J) / (3.00 x 10^8 m/s)^2
m ≈ 6.639 x 10^-19 kg (rounded to three significant figures)
Alternatively, you can convert the mass from kilograms to grams by multiplying by 1,000:
m ≈ 6.639 x 10^-16 g
Therefore, the mass equivalent of 1 mole of photons with a wavelength of 671 nm is approximately 6.639 x 10^-16 grams.