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 525nm, how many photons are emitted per second?

Answer 1

`2.64* 10^(20)` photons are emitted per second.

Step-by-step explanation:

Let the number of photons emitted by bulb be 'n'.

Given:

Energy radiated by bulb per second (E) = 100 J

Wavelength of light emitted (λ) = 525 nm =
`525* 10^(-9)\ m`

We know that,

Energy of a photon is given as:

`E_0=(hc)/(\lambda)`

Where,

`h\to Planck's\ constant=6.626* 10^(-34)\ Js\\\\c\to Speed\ of \ light=3* 10^(8)\ m/s`

Now, if there are 'n' photons, the energy will be equal to energy of 1 photon times the number of photons. So,

`E=nE_0\\\\E=(nhc)/(\lambda)`

Now, rewriting in terms of 'n', we get:

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

Plug in the values given and solve for 'n'. This gives,

`n=(100* 525* 10^(-9))/(6.626* 10^(-34)* 3* 10^(8))\\\\n=2.64* 10^(20)`

Therefore,
`2.64* 10^(20)` photons are emitted per second.