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

Answer:

$2.64\times 10^{20}$ photons are emitted per second.

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 = $525\times 10^{-9}\ m$

We know that,

Energy of a photon is given as:

$E_0=\frac{hc}{\lambda}$

Where,

$h\to Planck's\ constant=6.626\times 10^{-34}\ Js\\\\c\to Speed\ of \ light=3\times 10^{8}\ m/s$

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

$E=nE_0\\\\E=\frac{nhc}{\lambda}$

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

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

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

$n=\frac{100\times 525\times 10^{-9}}{6.626\times 10^{-34}\times 3\times 10^{8}}\\\\n=2.64\times 10^{20}$

Therefore, $2.64\times 10^{20}$ photons are emitted per second.