Question

A typical 100-watt light bulb consumes 100 j of energy per second. If a light bulb converts all of this energy to 400 nm light

Answer 1

The missing question is: how many photons are produced per second?

Answer:

$2.0\cdot 10^{20}$

Explanation:

The energy of a photon is given by

$E_1 = \frac{hc}{\lambda}$

where

h is the Planck constant

c is the speed of light

$\lambda$ is the wavelength of the photon

In this problem, the photons have wavelength

$\lambda = 400 nm = 400 \cdot 10^{-9} m$, so each photon has an energy of

$E_1 = \frac{(6.63\cdot 10^{-34})(3\cdot 10^8)}{400\cdot 10^{-9}}=4.97\cdot 10^{-19} J$

The total energy emitted by the bulb in 1 second is

E = 100 J

Therefore, the number of photons emitted per second is

$n=\frac{E}{E_1}=\frac{100}{4.97\cdot 10^{-19}}=2.0\cdot 10^{20}$

Answer 2

If 100W light bulb converts all of the energy to 400 nm light then the number of photons emitted per second is 2 x 10²⁰.

What is energy?

Energy is the capacity of doing work.

We know that the energy of a photon is given by the formula,

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

where h is the Planck constant, c is the speed of light, and λ is the wavelength of the photon.

Now, the photons have a wavelength

λ = 400 nm = 400 x 10⁻⁹ m,

So each of the photons has the energy of

$E=\dfrac{6.63 \times 10^{-34} \times 3 \times 10^8}{400 \times 10^{-9}}\\\\E = 4.97 \times 10^{-19}\rm\ J$

Further, It is given that the total energy emitted by the bulb in 1 second is E = 100 J. Thus, the number of photons emitted per second is

$n = \dfrac{E}{E_1} =\dfrc{100}{4.97 \times 10^{-19}}=2 \times 10^{20}$

Hence, If a 100W light bulb converts all of the energy to 400 nm light then the number of photons emitted per second is 2 x 10²⁰.

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