Question

A mole of yellow photons of wavelength 527 nm has __________ kj of energy.

Answer 1

Explanation:

It is known that relation between energy and wavelength is as follows.

            E = $\frac{hc}{\lambda}$

where,    h = plank's constant = $6.626 \times 10^{-34}$

              c = speed of light = $3 \times 10^{8} m/s^{2}$

          $\lambda$ = wavelength

Convert nm into m as follows.

                       $527 nm \times \frac{1 \times 10^{-9} m}{1 nm}$

                       = $527 \times 10^{-9}$ m

Therefore, calculate the energy as follows.

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

                    = $\frac{6.626 \times 10^{-34} \times 3 \times 10^{8} m/s^{2}}{527 \times 10^{-9}}$

                    = $0.037719 \times 10^{-17}$ J

Hence, energy of the yellow light is $0.037719 \times 10^{-17}$ J.

Now, calculate the moles of yellow light as follows.

          $0.037719 \times 10^{-17} \times 6.022 \times 10^{23}$  

               = $0.227144 \times 10^{6}$ J

               = 227144 J

or,           = 227.14 kJ        (as 1 kJ = 1000 J)

Thus, we can conclude that a mole of yellow photons of wavelength 527 nm has 227.14 kJ of energy.

Answer 2

227kj Because The first thing to do here is to calculate the energy of a single photon of wavelength equal to
527 nm
, then use Avogadro's number to scale this up to the energy of a mole of such photons.