Final answer:
The ratio of the number of X-ray photons to visible light photons emitted by two 100W sources with wavelengths of 1 nm and 500 nm, respectively, is approximately 1:1667.
Step-by-step explanation:
To find the ratio of the number of photons of X-rays to the photons of visible light emitted by two sources with equal power, but different wavelengths, we need to use the energy formula of a photon, which is E = hc/λ, where h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3.00 x 108 m/s), and λ is the wavelength of light.
The energy of one X-ray photon with a wavelength of 1 nm (1 x 10-9 m) can be calculated as:
EX-ray = (6.626 x 10-34 J·s)(3.00 x 108 m/s) / (1 x 10-9 m)= 6.626 x 10-16 J
Similarly, for a visible light photon with a wavelength of 500 nm (5 x 10-7 m):
Evisible = (6.626 x 10-34 J·s)(3.00 x 108 m/s) / (5 x 10-7 m) = 3.978 x 10-19 J
Since each source emits 100 W of power:
Number of X-ray photons per second = Power / Energy per photon
= 100 W / 6.626 x 10-16 J
= 1.51 x 1017 photons/s
Number of visible light photons per second = 100 W / 3.978 x 10-19 J = 2.51 x 1020 photons/s
Therefore, the ratio of X-ray photons to visible light photons is:
Ratio = Number of X-ray photons per second / Number of visible light photons per second
= (1.51 x 1017) / (2.51 x 1020) which simplifies to approximately 1:1667.