Question

Determine the energy of 1.70 mol of photons for each of the following kinds of light. (Assume three significant figures.)PART A infrared radiation (1600 nm)PART B visible light (505 nm )PART C ultraviolet radiation (150 nm )

Answer 1

Answer:

For A: The energy of the given amount of photons for infrared radiation is $1.271\times 10^5J$

For B: The energy of the given amount of photons for infrared radiation is $4.026\times 10^5J$

For C: The energy of the given amount of photons for infrared radiation is $1.355\times 10^6J$

Explanation:

The relationship between energy and frequency is given by Planck's equation, which is:

$E=n\rimes N_A\times \frac{hc}{\lambda}$        ......(1)

where,

h = Planck's constant  = $6.62\times 10^{-34}Js$

E = energy of the light

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

$\lambda$ = wavelength of light

$N_A$ = Avogadro's number = $6.022\times 10^{23}$

n = number of moles of photons = 1.70 moles

Conversion factor used:  $1m=10^9nm$

• For A:

Wavelength of infrared radiation = $1600nm=1.6\times 10^6m$

Putting values in equation 1, we get:

$E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{1.6\times 10^{-6}}\\\\E=1.271\times 10^5J$

Hence, the energy of the given amount of photons for infrared radiation is $1.271\times 10^5J$

• For B:

Wavelength of visible light = $505nm=5.05\times 10^7m$

Putting values in equation 1, we get:

$E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{5.05\times 10^{-7}}\\\\E=4.026\times 10^5J$

Hence, the energy of the given amount of photons for infrared radiation is $4.026\times 10^5J$

• For C:

Wavelength of ultraviolet radiation = $150nm=1.5\times 10^7m$

Putting values in equation 1, we get:

$E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{1.5\times 10^{-7}}\\\\E=1.355\times 10^6J$

Hence, the energy of the given amount of photons for infrared radiation is $1.355\times 10^6J$