Answer :
(1) The frequency of photon is, ![3\times 10^{10}Hz](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E%7B10%7DHz)
(2) The energy of a single photon of this radiation is ![1.988\times 10^{-23}J/photon](https://tex.z-dn.net/?f=1.988%5Ctimes%2010%5E%7B-23%7DJ%2Fphoton)
(3) The energy of an Avogadro's number of photons of this radiation is, 11.97 J/mol
Explanation : Given,
Wavelength of photon =
(1 m = 100 cm)
(1) Now we have to calculate the frequency of photon.
Formula used :
![\nu=\frac{c}{\lambda}](https://tex.z-dn.net/?f=%5Cnu%3D%5Cfrac%7Bc%7D%7B%5Clambda%7D)
where,
= frequency of photon
= wavelength of photon
c = speed of light = ![3\times 10^8m/s](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E8m%2Fs)
Now put all the given values in the above formula, we get:
![\nu=\frac{3\times 10^8m/s}{0.01m}](https://tex.z-dn.net/?f=%5Cnu%3D%5Cfrac%7B3%5Ctimes%2010%5E8m%2Fs%7D%7B0.01m%7D)
![(1Hz=1s^{-1})](https://tex.z-dn.net/?f=%281Hz%3D1s%5E%7B-1%7D%29)
The frequency of photon is, ![3\times 10^{10}Hz](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E%7B10%7DHz)
(2) Now we have to calculate the energy of photon.
Formula used :
![E=h\times \nu](https://tex.z-dn.net/?f=E%3Dh%5Ctimes%20%5Cnu)
where,
= frequency of photon
h = Planck's constant = ![6.626\times 10^{-34}Js](https://tex.z-dn.net/?f=6.626%5Ctimes%2010%5E%7B-34%7DJs)
Now put all the given values in the above formula, we get:
![E=(6.626\times 10^{-34}Js)\times (3\times 10^{10}s^{-1})](https://tex.z-dn.net/?f=E%3D%286.626%5Ctimes%2010%5E%7B-34%7DJs%29%5Ctimes%20%283%5Ctimes%2010%5E%7B10%7Ds%5E%7B-1%7D%29)
![E=1.988\times 10^{-23}J/photon](https://tex.z-dn.net/?f=E%3D1.988%5Ctimes%2010%5E%7B-23%7DJ%2Fphoton)
The energy of a single photon of this radiation is ![1.988\times 10^{-23}J/photon](https://tex.z-dn.net/?f=1.988%5Ctimes%2010%5E%7B-23%7DJ%2Fphoton)
(3) Now we have to calculate the energy in J/mol.
![E=1.988\times 10^{-23}J/photon](https://tex.z-dn.net/?f=E%3D1.988%5Ctimes%2010%5E%7B-23%7DJ%2Fphoton)
![E=(1.988\times 10^{-23}J/photon)\times (6.022\times 10^{23}photon/mol)](https://tex.z-dn.net/?f=E%3D%281.988%5Ctimes%2010%5E%7B-23%7DJ%2Fphoton%29%5Ctimes%20%286.022%5Ctimes%2010%5E%7B23%7Dphoton%2Fmol%29)
![E=11.97J/mol](https://tex.z-dn.net/?f=E%3D11.97J%2Fmol)
The energy of an Avogadro's number of photons of this radiation is, 11.97 J/mol