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 [tex]T_1[/tex] = 20.0° C
the final temperature [tex]T_2[/tex] = 99° C
Change in temperature [tex]\Delta T[/tex] = (99-20)° C = 79 ° C
The heat q absorbed during the process = ms [tex]\Delta T[/tex]
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 = [tex]6.626 \times 10^{-34} \ J.s[/tex]
c = velocity of light = [tex]3.0 \times 10^8 \ m/s[/tex]
= [tex]\dfrac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{0.125}[/tex]
= [tex]1.59024 \times 10^{-24}[/tex] J
The total photons required = Total heat energy/ Energy of a photon
The total photons required = [tex]\dfrac{82555 J}{1.59024 \times 10^{-24}J}[/tex]
The total photons required = 5.19 × 10²⁸ photons
