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

Answer 2

The number of photons emitted per second will be "$2.6\times 10^{20}$".

According to the question'

Energy,

• E = 100 J

Planks constant,

• h = $6.63\times 10^{-34} \ J.s$

Velocity of light,

• c = $3\times 10^8 \ m/s$

Wavelength,

• λ = 525 nm

or,

           = $525\times \frac{10^{-9}}{1}$

           = $5.25\times 10^{-7} \ m$

As we know,

→ Energy, $E = n \frac{hc}{\lambda}$

The number of photons will be:

= $\frac{E \lambda}{hc}$

= $\frac{100(5.25\times 10^{-7})}{(6.63\times 10^{-34})(3\times 10^8)}$

= $2.6\times 10^{20}$

Thus the above solution is correct.

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