<u>Answer:</u>
<u>For A:</u> The energy of the given amount of photons for infrared radiation is ![1.271\times 10^5J](https://tex.z-dn.net/?f=1.271%5Ctimes%2010%5E5J)
<u>For B:</u> The energy of the given amount of photons for infrared radiation is ![4.026\times 10^5J](https://tex.z-dn.net/?f=4.026%5Ctimes%2010%5E5J)
<u>For C:</u> The energy of the given amount of photons for infrared radiation is ![1.355\times 10^6J](https://tex.z-dn.net/?f=1.355%5Ctimes%2010%5E6J)
<u>Explanation:</u>
The relationship between energy and frequency is given by Planck's equation, which is:
......(1)
where,
h = Planck's constant = ![6.62\times 10^{-34}Js](https://tex.z-dn.net/?f=6.62%5Ctimes%2010%5E%7B-34%7DJs)
E = energy of the light
c = speed of light = ![3\times 10^8m/s](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E8m%2Fs)
= wavelength of light
= Avogadro's number = ![6.022\times 10^{23}](https://tex.z-dn.net/?f=6.022%5Ctimes%2010%5E%7B23%7D)
n = number of moles of photons = 1.70 moles
Conversion factor used: ![1m=10^9nm](https://tex.z-dn.net/?f=1m%3D10%5E9nm)
Wavelength of infrared radiation = ![1600nm=1.6\times 10^6m](https://tex.z-dn.net/?f=1600nm%3D1.6%5Ctimes%2010%5E6m)
Putting values in equation 1, we get:
![E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{1.6\times 10^{-6}}\\\\E=1.271\times 10^5J](https://tex.z-dn.net/?f=E%3D1.7%5Ctimes%206.022%5Ctimes%2010%5E%7B23%7D%5Ctimes%20%5Cfrac%7B6.62%5Ctimes%2010%5E%7B-34%7D%5Ctimes%203%5Ctimes%2010%5E8%7D%7B1.6%5Ctimes%2010%5E%7B-6%7D%7D%5C%5C%5C%5CE%3D1.271%5Ctimes%2010%5E5J)
Hence, the energy of the given amount of photons for infrared radiation is ![1.271\times 10^5J](https://tex.z-dn.net/?f=1.271%5Ctimes%2010%5E5J)
Wavelength of visible light = ![505nm=5.05\times 10^7m](https://tex.z-dn.net/?f=505nm%3D5.05%5Ctimes%2010%5E7m)
Putting values in equation 1, we get:
![E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{5.05\times 10^{-7}}\\\\E=4.026\times 10^5J](https://tex.z-dn.net/?f=E%3D1.7%5Ctimes%206.022%5Ctimes%2010%5E%7B23%7D%5Ctimes%20%5Cfrac%7B6.62%5Ctimes%2010%5E%7B-34%7D%5Ctimes%203%5Ctimes%2010%5E8%7D%7B5.05%5Ctimes%2010%5E%7B-7%7D%7D%5C%5C%5C%5CE%3D4.026%5Ctimes%2010%5E5J)
Hence, the energy of the given amount of photons for infrared radiation is ![4.026\times 10^5J](https://tex.z-dn.net/?f=4.026%5Ctimes%2010%5E5J)
Wavelength of ultraviolet radiation = ![150nm=1.5\times 10^7m](https://tex.z-dn.net/?f=150nm%3D1.5%5Ctimes%2010%5E7m)
Putting values in equation 1, we get:
![E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{1.5\times 10^{-7}}\\\\E=1.355\times 10^6J](https://tex.z-dn.net/?f=E%3D1.7%5Ctimes%206.022%5Ctimes%2010%5E%7B23%7D%5Ctimes%20%5Cfrac%7B6.62%5Ctimes%2010%5E%7B-34%7D%5Ctimes%203%5Ctimes%2010%5E8%7D%7B1.5%5Ctimes%2010%5E%7B-7%7D%7D%5C%5C%5C%5CE%3D1.355%5Ctimes%2010%5E6J)
Hence, the energy of the given amount of photons for infrared radiation is ![1.355\times 10^6J](https://tex.z-dn.net/?f=1.355%5Ctimes%2010%5E6J)