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Sagot :
The photon which is required to raise the temperature of 2.1 gm of water by 1.7 kk is 2.16 x [tex]10^{20} photons[/tex]
Given the following data:
Mass of water = [tex]2.1 gm[/tex]
Change in temperature = [tex]1.7 Kelvin[/tex]
Wavelength of infrared = [tex]2.9[/tex] х [tex]10^{-4} cm[/tex]
Specific heat capacity of water = 4.18 J/g°K.
Conversion:
100 cm = 1 m
[tex]2.9 X 10^{-4} cm = 2.9 X 10^{-6}[/tex]
To find the amount of photons required to raise the temperature of 2.1 g of water:
First of all, we would determine the quantity of energy required to raise the temperature of water:
Mathematically, quantity of energy is given by the formula;
[tex]Q = mc[/tex]θ
Where:
Q represents the quantity of energy.
m represents the mass of an object.
c represents the specific heat capacity.
∅ represents the change in temperature.
Substituting the given parameters into the formula, we have;
[tex]Q = 2.1(4.18)(1.7)\\\\Q = 14.92 Joules[/tex]
Mathematically, the Planck-Einstein relation is given by the formula:
[tex]E = hf[/tex]
Where:
h is Planck constant.
f is photon frequency.
To find the photon frequency, we would use this formula:
[tex]Photon frequency = \frac{speed}{wavelength} \\\\Photon frequency = \frac{3(10^{8} )}{2.9(10^{-6} )}\\ \\Photon frequency = \frac{300000000}{0.0000029}\\ \\Photon frequency = 1.04 X 10^{14} Hz[/tex]
Applying Planck-Einstein's relation, we would determine the energy required by each of photon:
[tex]E = 6.626[/tex] х [tex]10^{-34}[/tex] х [tex]1.04[/tex] х [tex]10^{14}[/tex]
[tex]E= 6.89[/tex] х [tex]10^{-20} Joules[/tex]
Now, we can calculate the amount of photons required to raise the temperature of 2.1 g of water by using this expression:
[tex]Number of photons = \frac{Q}{E} \\\\Number of photons = \frac{14.92}{6.89(10^{-20} )}\\ \\Number of photons = 2.16 X 10^{20} photons[/tex]
Disclaimer: Given Question is incomplete, please find the correct question:
Water is exposed to infrared radiation of wavelength 2.9x10-4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons will be required to raise the temperature of 2.1 g of water by 1.7 K? Express your answer using two significant figures.
Thus the concluded that number of photon is 2.16 x [tex]10^{20}[/tex] photons.
learn more about wavelength:
https://brainly.com/question/4112024
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