Respuesta :
E = h * c / lambda where
E is the energy
h is Plack's constant, h = 6.626 × 10 -34 joule·s
c is the speed of light in m/sec
lambda is the wavelength.
The total energy required = mass of water * specific heat * temperature change
Divide the total energy by the energy per photon.
E is the energy
h is Plack's constant, h = 6.626 × 10 -34 joule·s
c is the speed of light in m/sec
lambda is the wavelength.
The total energy required = mass of water * specific heat * temperature change
Divide the total energy by the energy per photon.
Answer: The number of photons absorbed by the water is [tex]6.59\times 10^{28}[/tex]
Explanation:
- To calculate the energy of 1 photon, we use the equation:
[tex]E=\frac{hc}{\lambda}[/tex]
where,
E = energy of the photon
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
c = speed of light = [tex]3.0\times 10^8m/s[/tex]
[tex]\lambda[/tex] = wavelength of photon = 13.3 cm = 0.133 m (Conversion factor: 1 m = 100 cm )
Putting values in above equation, we get:
[tex]E=\frac{6.626\times 10^{-34}Js\times 3.0\times 10^8m/s}{0.133m}\\\\E=1.495\times 10^{-24}J[/tex]
To calculate the mass of water, we use the equation:
[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]
Density of water = 1 g/mL
Volume of water = 0.317 L = 317 mL (Conversion factor: 1 L = 1000 mL )
Putting values in above equation, we get:
[tex]1g/mL=\frac{\text{Mass of water}}{317mL}\\\\\text{Mass of water}=(1g/mL\times 317mL)=317g[/tex]
- To calculate the amount of energy absorbed, we use the equation:
[tex]q=mc\Delta T[/tex]
where,
q = heat absorbed
m = mass of water = 317 g
c = specific heat capacity of water = 4.184 J/g°C
[tex]\Delta T[/tex] = change in temperature = 74.3°C
Putting values in above equation, we get:
[tex]q=317g\times 4.184J/g^oC\times 74.3^oC=98546.2J[/tex]
- To calculate the number of photons, we divide the amount of energy absorbed by the energy of 1 photon, which is:
[tex]\text{Number of photons}=\frac{\text{Total amount of energy absorbed}}{\text{Energy of 1 photon}}[/tex]
Putting values in above equation, we get:
[tex]\text{Number of photons}=\frac{98546.2J}{1.495\times 10^{-24}J}=6.59\times 10^{28}[/tex]
Hence, the number of photons absorbed by the water is [tex]6.59\times 10^{28}[/tex]
