Question

What is the wavelength, speed of associated with a light transmitted through in water at 6.66z10¹⁴ Hz? Also report the energy in Joules, eV, and wavenumber per photon. (n(water)=1.33)

Answer 1

Answer:

Speed of light in vacuum = 3.0 x 10⁸ m/s

Speed of light in a medium with refractive index n = (3.0 x 10⁸ m/s) / n

So speed of light in water (where n = 1.33) = (3.0 x 10⁸ m/s) / 1.33 = 2.25 x 10⁸ m/s

Energy of photon = hv

Where

h = Planck's constant = 6.626 x 10^-34 Js

v = frequency of photon = 6.66 x 10¹⁴ Hz

So, energy of photon = hv = (6.626 x 10^-34 Js) x (6.66 x 10¹⁴ Hz) = 4.413 x 10^-19 J

1 eV = 1.6 x 10^-19 J

So energy of the photon in eV = 4.413 x 10^-19 J / (1.6 x 10^-19 J / eV) = 2.76 eV

Wavenumber is amount of oscillations of field exist in 1 m (or 1 cm) length.

wavenumber = 1 / wavelength = frequency of light / speed of light in cm

wavenumber = 6.66 x 10¹⁴ Hz / (3.0 x 10¹⁰ m/s) = 2.22 x 10⁴ cm^-1