Question

A sodium lamp emits at 589 nm (yellow light). If you place a sodium lamp above a bowl that contains 350 mL water, how many photons must be absorbed to raise temperature of the water by 20 degrees celcius? Assume no energy from the contents of the bowl is lost to the surrounding, and the density of water is 1.00 g/mL. The heat capacity of water is 4.184 J/g degrees celcius

Answer 1

To raise the temperature of the water, the number of photons that must be absorbed can be calculated using the equation: Number of photons = Energy required / Energy per photon. Substituting the given values, the number of photons required to raise the temperature of the water is approximately 8.69 x 10^21 photons.

Step-by-step explanation:

To calculate the number of photons that must be absorbed to raise the temperature of the water, we need to use the formula:

Number of photons = Energy required / Energy per photon

First, we need to calculate the energy required. The heat capacity of water is given as 4.184 J/g degrees Celsius, so the energy required can be calculated as:

Energy required = Mass of water x Specific heat of water x Change in temperature

Substituting the given values, the energy required is:

Energy required = 350 g x 4.184 J/g °C x 20 °C

= 29,288 J

The average photon energy can be calculated using the equation:

Energy per photon = Planck's constant x Speed of light / Wavelength

Substituting the given values, the average photon energy is approximately 3.36 x 10^-19 J.

Finally, we can calculate the number of photons:

Number of photons = 29,288 J / 3.36 x 10^-19 J

= 8.69 x 10^21 photons