Answer:
The total photons required = 5.19 × 10²⁸ photons
Explanation:
Given that:
the radiation wavelength λ= 12.5 cm = 0.125 m
Volume of the container = 0.250 L = 250 mL
The density of water = 1 g/mL
Density = mass /volume
Mass = Volume × Density
Thus; the mass of the water = 250 mL × 1 g/mL
the mass of the water = 250 g
the specific heat of water s = 4.18 J/g° C
the initial temperature
= 20.0° C
the final temperature
= 99° C
Change in temperature
= (99-20)° C = 79 ° C
The heat q absorbed during the process = ms
The heat q absorbed during the process = 250 g × 4.18 J/g° C × 79° C
The heat q absorbed during the process = 82555 J
The energy of a photon can be represented by the equation :
= hc/λ
where;
h = planck's constant = ![6.626 \times 10^{-34} \ J.s](https://tex.z-dn.net/?f=6.626%20%5Ctimes%2010%5E%7B-34%7D%20%5C%20J.s)
c = velocity of light = ![3.0 \times 10^8 \ m/s](https://tex.z-dn.net/?f=3.0%20%5Ctimes%2010%5E8%20%5C%20m%2Fs)
= ![\dfrac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{0.125}](https://tex.z-dn.net/?f=%5Cdfrac%7B6.626%20%5Ctimes%2010%5E%7B-34%7D%20%5Ctimes%203.0%20%5Ctimes%2010%5E8%7D%7B0.125%7D)
=
J
The total photons required = Total heat energy/ Energy of a photon
The total photons required = ![\dfrac{82555 J}{1.59024 \times 10^{-24}J}](https://tex.z-dn.net/?f=%5Cdfrac%7B82555%20J%7D%7B1.59024%20%5Ctimes%2010%5E%7B-24%7DJ%7D)
The total photons required = 5.19 × 10²⁸ photons