Water is exposed to infrared radiation of wavelength 2.5×10−4 cm. Assume that all the radiation is absorbed and converted to heat.
How many photons will be required to raise the temperature of 2.5 g of water by 2.5 K?
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I tried solving this problem on my own, and I got 3.3 x 10^-30 photons, which was incorrect.
What is the amount of energy needed to raise the T of H2O.
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q in J = 2.5g x 4.184J/g*K x 2.5K = about 26 J but you should do it more accurately.
How much energy do we obtain from one photon. That's E = hc/wavelength
E= joules/photon = 6.626E-34 J.s x 3E8 m/2.4E-6 m = about 8E-20 J.
So 8E-20J/photon x no. photons = 26 J
Solve for #photons.
I am not sure how to solve for photons. I tried dividing the 8E-20 J/photon and 26 J, but I was incorrect.
Did you redo the 26 J? That's isn't the exact number. Did you redo 8.2E-20 J/photon? That isn't the exact number.
After you correct the numbers, then
#photons = 26?/8.2E-20? = xx
I was having problems fining the "exact" value of 8.2E-20. I actually got 8.285E-32. As for the 26, the exact value is 26.15. I divided those two numbers together, and my response was still wrong.
To solve this problem, you need to use the formula that relates the energy of a photon to its wavelength:
E = hc / λ
where E is the energy of the photon, h is the Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength of the radiation.
First, we need to convert the wavelength to meters:
λ = 2.5 x 10^-4 cm = 2.5 x 10^-6 m
Next, we can calculate the energy of each photon using the formula:
E = (6.626 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (2.5 x 10^-6 m)
E = 7.9472 x 10^-19 J
We know that the amount of energy needed to raise the temperature of 1 gram of water by 1 Kelvin is approximately 4.186 J. Therefore, the amount of energy needed to raise the temperature of 2.5 grams of water by 2.5 K is:
(4.186 J/g·K) * (2.5 g) * (2.5 K) = 26.1625 J
Finally, we can calculate the number of photons required by dividing the total energy needed by the energy of each photon:
Number of photons = (26.1625 J) / (7.9472 x 10^-19 J)
Number of photons ≈ 3.29 x 10^19 (rounded to two significant figures)
Hence, the correct answer is approximately 3.29 x 10^19 photons.