Question

A 100-watt light bulb radiates energy at a rate of 100 J/s. (The watt, a unit of power or energy over time, is defined as 1 J/s.) If all of the light emitted has a wavelength of 525 nm , how many photons are emitted per second?

Answer 1

Answer

2.7956 * 10^19 photons

Givens

• Wavelength = λ = 525 * 10^-9 meters  [1 nmeter = 1*10^-9 meters]
• c = 3 * 10^8 meters
• E = ???
• W = 100  watts
• t = 1 second
• h= plank's Constant = 6.26 * 10^-34 J*s

Formula

E = h * c / λ

W = E / t

Solution

E = 6.26 * 10^-34 j*s * 3 * 10^8 m/s /525 * 10^-9 (m)

The meters cancel out. So do the seconds. You are left with Joules as you should be.

E =  3.577 * 10^-18 Joules

What you have found is the energy of 1 photon.

Now you have to find the Joules from the watts.

W = E/t

100 * 1 second = 100 joules

1 photon contains 3.577 * 10 ^ - 18 Joules

x photon = 100 joules                        

1/x = 3.577 * 10^-18 / 100                          Cross multiply

100 = 3.577 * 10 ^ - 18 * x                         Divide both sides by 3.577 * 10 ^ - 18

100/3.577 * 10 ^ - 18 = 3.577 * 10 ^ - 18x / 3.577 * 10 ^ - 18

2.7956 * 10^19 photons = x