Question

A container with 0.317 L of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 13.3 cm. The temperature of the water then rose by 74.3 °C. Calculate the number of photons that were absorbed by the water. Assume water has a density of 1.00 g·mL–1 and its specific heat is 4.184 J·g–1·°C–1

Answer 1

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.

Answer 2

Answer: The number of photons absorbed by the water is
`6.59* 10^(28)`

Step-by-step explanation:

• To calculate the energy of 1 photon, we use the equation:

`E=(hc)/(\lambda)`

where,

E = energy of the photon

h = Planck's constant =
`6.626* 10^(-34)Js`

c = speed of light =
`3.0* 10^8m/s`

`\lambda` = wavelength of photon = 13.3 cm = 0.133 m (Conversion factor: 1 m = 100 cm )

Putting values in above equation, we get:

`E=(6.626* 10^(-34)Js* 3.0* 10^8m/s)/(0.133m)\\\\E=1.495* 10^(-24)J`

To calculate the mass of water, we use the equation:

`\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}`

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:

`1g/mL=\frac{\text{Mass of water}}{317mL}\\\\\text{Mass of water}=(1g/mL* 317mL)=317g`

• To calculate the amount of energy absorbed, we use the equation:

`q=mc\Delta T`

where,

q = heat absorbed

m = mass of water = 317 g

c = specific heat capacity of water = 4.184 J/g°C

`\Delta T` = change in temperature = 74.3°C

Putting values in above equation, we get:

`q=317g* 4.184J/g^oC* 74.3^oC=98546.2J`

• To calculate the number of photons, we divide the amount of energy absorbed by the energy of 1 photon, which is:

`\text{Number of photons}=\frac{\text{Total amount of energy absorbed}}{\text{Energy of 1 photon}}`

Putting values in above equation, we get:

`\text{Number of photons}=(98546.2J)/(1.495* 10^(-24)J)=6.59* 10^(28)`

Hence, the number of photons absorbed by the water is
`6.59* 10^(28)`