Estimate the number of photons emitted by the Sun in a second. The power output from the Sun is 4 × 10²⁶ W and assume that the average wavelength of each photon is 550 nm. A) 10²⁶ B) 10⁴⁵ C) 10²³ D) 10²⁸ E) None of the above.

Question

Quizplus · Accepted Answer

First, we need to find the energy of each photon using the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the average wavelength. Substituting the given values, we get:
E = (6.626 x 10^-34 J s)(2.998 x 10^8 m/s)/(550 x 10^-9 m) = 3.6 x 10^-19 J

Next, we can find the number of photons using the equation power = energy x frequency, where power is given and frequency is c/λ. Substituting the given values, we get:
4 x 10^26 W = (3.6 x 10^-19 J/photon)(2.998 x 10^8 m/s)/(550 x 10^-9 m) x number of photons
Solving for number of photons, we get:
number of photons = 7.8 x 10^41 photons/s

The closest answer choice to this value is B: 10^45, which is the same as 1 x 10^45.

Estimate the Number of Photons Emitted by the Sun in a Second