Question

a 100 - watt lightbulb produces about 10 joules of visible energy each second. assuming the light emitted is green with a wave frequency of 600 trillion hertz (6×1014 hz), how many photons are produced each second the bulb is lit?
a. 3.98e - 19
b. 2.55e25
c. 6.2e14
d. 2.51e19

Explanation:

Step1: Calculate the energy of a single photon

The energy of a photon is given by the formula \(E = hf\), where \(h = 6.626\times10^{-34}\space J\cdot s\) (Planck's constant) and \(f = 6\times 10^{14}\space Hz\) (frequency).

$$E=(6.626\times 10^{-34}\space J\cdot s)\times(6\times 10^{14}\space Hz)=3.9756\times 10^{-19}\space J$$

Step2: Calculate the number of photons

If the total energy emitted per second \(E_{total}=10\space J\), and the energy of a single photon \(E = 3.9756\times 10^{-19}\space J\), then the number of photons \(n=\frac{E_{total}}{E}\)

$$n=\frac{10\space J}{3.9756\times 10^{-19}\space J}\approx2.51\times 10^{19}$$

Answer:

d. \(2.51E19\)