Question

Water is exposed to infrared radiation of wavelength 3.0×10^−4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons will be required to raise the temperature of 1.6 g of water by 2.5 K?

A) 3.0 × 10²3 photons
B) 6.02 × 10²3 photons
C) 1.2 × 10²4 photons
D) 2.5 × 10²5 photons

Answer 1

To calculate the number of photons required to raise the temperature of water, we can use the equation energy of one photon equals Planck's constant times the speed of light divided by the wavelength. By plugging in the values, we find that the number of photons required is approximately 1.2 x 10^4.

Step-by-step explanation:

To calculate the number of photons required to raise the temperature of water, we can use the equation:

Energy of one photon = Planck's constant (h) x speed of light (c) / wavelength

Now we can calculate the energy of one photon:

Energy of one photon = (6.626 x 10^-34 Js) x (3.0 x 10^8 ms^-1) / (3.0 x 10^-4 cm)

Next, we can calculate the total energy requireda to raise the temperature of the water:

Total energy required = mass x specific heat x temperature change

Using the given values, we can calculate the total energy required as well as the number of photons:

Total energy required = (1.6 g) x (4.184 J/g°C) x (2.5 K)

Number of photons = Total energy required / Energy of one photon

By plugging in the values, we find that the answer is approximately 1.2 x 10^4 photons. Therefore, the correct answer is C) 1.2 x 10^4 photons.