A sodium vapor lamp has a power output of 300 W.If 590 nm is the average wavelength of the source,about how many photons are emitted per second? (h = 6.63 x 10^-34 J*s,c = 3.00 x 10⁸ m/s,and 1 nm = 10^-9 m) A)10¹⁷ B)10²¹ C)10²⁵ D)10²⁹

Question

Quizplus · Accepted Answer

First, we need to find the energy of a single photon with the given wavelength.
Using the formula:
E = hc/λ
where h is Planck's constant, c is the speed of light, and λ is the wavelength
E = (6.63 x 10^-34 J s)(3.00 x 10^8 m/s)/(590 x 10^-9 m)
E = 3.36 x 10^-19 J
Next, we can find the number of photons emitted per second using the power of the lamp and the energy per photon.
Using the formula:
Power = Energy per photon x Number of photons per second
Number of photons per second = Power/Energy per photon
Number of photons per second = (300 W)/(3.36 x 10^-19 J)
Number of photons per second = 8.93 x 10^20
Rounding to three significant figures gives 1.21 x 10^21 or 10^21 photons per second, which corresponds to choice B.

A Sodium Vapor Lamp Has a Power Output of 300