Question

Careful spectral analysis shows that the familiar yellow light of sodium lamps (such as street lamps) is made up of photons of two wavelengths, 589.0 nm and 589.6 nm. What is the difference in energy (in joules/mol) between one mole of photons with these wavelengths?

Answer 1

Answer : The energy difference for one mole of photon is 206.55 J/mol.

Explanation :

Formula used :

$E=\frac{hc}{\lambda}$

For two different wavelength the formula will be:

$E_1=\frac{hc}{\lambda_1}$

$E_2=\frac{hc}{\lambda_2}$

$\Delta E=E_1-E_2=\frac{hc}{\lambda_1}-\frac{hc}{\lambda_2}$

$\Delta E=hc\times [\frac{1}{\lambda_1}-\frac{1}{\lambda_2}]$

where,

$\Delta E$ = difference in energy of photon = ?

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $3\times 10^8m/s$

$\lambda_1$ = wavelength of photon 1 = 589.0 nm = $589\times 10^{-9}m$

conversion used : $1nm=10^{-9}m$

$\lambda_2$ = wavelength of photon 2 = 589.6 nm = $589.6\times 10^{-9}m$

Now put all the given values in the above formula, we get:

$\Delta E=(6.626\times 10^{-34}Js)\times (3\times 10^8m/s)\times [\frac{1}{589\times 10^{-9}m}-\frac{1}{589.6\times 10^{-9}m}]$

$\Delta E=3.43\times 10^{-22}J$

Energy difference for one mole of photon = $\Delta E\times \text{Avogadro's number}$

Energy difference for one mole of photon = $(3.43\times 10^{-22}J)\times (6.022\times 10^{23})=206.55J/mol$

Therefore, the energy difference for one mole of photon is 206.55 J/mol.

Answer 2

Thank you for posting your question here at brainly. Below is the solution:

Use the following relation: dE = h ( f2 - f1), where dE is the difference in the energy, h is the Planck's Constant and f1, f2 are the given frequencies. 

dE = 6.626 X 10^ -34 ( 589.6 - 589) = 3.9756e-34