Respuesta :
Answer: The number of photons are [tex]3.7\times 10^8[/tex]
Explanation:
We are given:
Wavelength of microwave = [tex]1.22\times 10^8nm=0.122m[/tex] (Conversion factor: [tex]1m=10^9nm[/tex] )
- To calculate the energy of one photon, we use Planck's equation, which is:
[tex]E=\frac{hc}{\lambda}[/tex]
where,
h = Planck's constant = [tex]6.625\times 10^{-34}J.s[/tex]
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\lambda[/tex] = wavelength = 0.122 m
Putting values in above equation, we get:
[tex]E=\frac{6.625\times 10^{-34}J.s\times 3\times 10^8m/s}{0.122m}\\\\E=1.63\times 10^{-24}J[/tex]
Now, calculating the energy of the photon with 88.3 % efficiency, we get:
[tex]E=1.63\times 10^{-24}\times \frac{88.3}{100}=1.44\times 10^{-24}J[/tex]
- To calculate the mass of water, we use the equation:
[tex]Density=\frac{Mass}{Volume}[/tex]
Density of water = 1 g/mL
Volume of water = 165 mL
Putting values in above equation, we get:
[tex]1g/mL=\frac{\text{Mass of water}}{165mL}\\\\\text{Mass of water}=165g[/tex]
- To calculate the amount of energy of photons to raise the temperature from 23°C to 100°C, we use the equation:
[tex]q=mc\Delta T[/tex]
where,
m = mass of water = 165 g
c = specific heat capacity of water = 4.184 J/g.°C
[tex]\Delta T[/tex] = change in temperature = [tex]T_2-T_1=100^oC-23^oC=77^oC[/tex]
Putting values in above equation, we get:
[tex]q=165g\times 4.184J/g.^oC\times 77^oC\\\\q=53157.72J[/tex]
This energy is the amount of energy for 'n' number of photons.
- To calculate the number of photons, we divide the total energy by energy of one photon, we get:
[tex]n=\frac{q}{E}[/tex]
q = 53127.72 J
E = [tex]1.44\times 10^{-24}J[/tex]
Putting values in above equation, we get:
[tex]n=\frac{53157.72J}{1.44\times 10^{-24}J}=3.7\times 10^{28}[/tex]
Hence, the number of photons are [tex]3.7\times 10^8[/tex]
A photon is a stable particle with no mass and no electric charge. A photon is a sort of elementary particle with zero rest mass and travels at the speed of light. The number of photons needed will be 3.7×10⁸.
What is a photon?
In the vacuum, a photon is a sort of elementary particle with zero rest mass and travels at the speed of light. To put it another way, it is the tiniest and most basic particle of electromagnetic energy.
The given data in the problem is;
( λ) is the wavelength of microwave = 1.22 ×10⁸ nm= 0.122 m.
h is Planck's constant = 6.625×10⁻³⁴ js
c is the speed of light = 3×10⁸ m/sec
Density of water = 1 g/mL
The volume of water = 165 mL
According to plank's equation,
[tex]E =\frac{hc}{\lambda}[/tex]
[tex]\rm E =\frac{6.625\times 10^{-34} \3\times10^8}{0.122}\\\\ \rm E= 1.63\times 10^{-24} J[/tex]
The energy of the photon with the efficiency of 83%,
[tex]\rm E =\frac{6.625\times 88}{100}\\\\ \rm E=1.44\times 10^{-24 }J[/tex]
[tex]\rm Mass \;of \;water={density \;of \;water}\times{volume \;of \;water} \\\\\ \rm Mass \;of \;water={1}\times{165}\\\\ \rm mass = 165 g[/tex]
the amount of energy of photons to raise the temperature from 23°C to 100°C will be
[tex]\rm{q= mcdt}[/tex]
m is the mass of water = 165 g
c is the specific heat capacity of water = 4.184 J/g.°C
dt is changed in temperature = 100°C-23°C = 77°C
[tex]\rm{q= mcdt}\\\\\rm{q= 165\times4.184\times77^0}\\\\\rm{q= 53157.52 \;J}[/tex]
A number of photons are equal to the ratio of total energy to the energy of one photon.
[tex]\rm{n = \frac{q}{E} }\\\\\rm{n = \frac{53127.72}{1.44\times 10^{-24}} }\\\\\rm{n = 3.7\times10^{28} }[/tex]
Hence the number of photons needed will be 3.7×10⁸.
To learn more about the photon refer to the link;
https://brainly.com/question/26523138
