the bright yellow light emitted by a sodium vapor lamp consists of two emission lines at 589.0 and 589.6 nm. what are the frequency and the energy of a photon of light at each of these wavelengths? what are the enegies in kJ/mol
c = wavelength x frequency.
You know c (speed of light is 3 x 10^8 m/s) and you know wavelength (change to meters). Calculate freqency in Herz.
E = hc/wavelength. That will give you the energy of 1 photon in Joules. Multiply by 6.02 x 10^23 to convert to Joules/mol of photons and change that to kJ/mol. Post your work if you get stuck.
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I believe you should divide by 6.022 x 10^23 moles?
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To determine the frequency of a photon, we can use the equation:
c = λν
Where:
c = speed of light (approximately 3.00 × 10^8 m/s)
λ = wavelength (in meters)
ν = frequency (in Hz)
Given that the two emission lines of the sodium vapor lamp are at 589.0 nm and 589.6 nm, we need to convert these wavelengths into meters by dividing by 10^9:
λ1 = 589.0 nm = 589.0 × 10^(-9) m
λ2 = 589.6 nm = 589.6 × 10^(-9) m
Now, we can calculate the frequency of each photon:
ν1 = c / λ1
ν2 = c / λ2
Substituting the values:
ν1 = (3.00 × 10^8 m/s) / (589.0 × 10^(-9) m)
ν2 = (3.00 × 10^8 m/s) / (589.6 × 10^(-9) m)
To calculate the energy of a photon, we can use the equation:
E = hν
Where:
E = energy of the photon (in Joules)
h = Planck's constant (approximately 6.626 × 10^(-34) J·s)
ν = frequency (in Hz)
Now, we can calculate the energy of each photon:
E1 = hν1
E2 = hν2
Finally, to convert the energies into kilojoules per mole, we need to multiply them by the Avogadro constant (6.022 × 10^23 mol^(-1)):
E1 (kJ/mol) = E1 × (6.022 × 10^23 mol^(-1))
E2 (kJ/mol) = E2 × (6.022 × 10^23 mol^(-1))
Now, you can plug the values into the equations to calculate the frequency and energy for each wavelength.