A particular form of electromagnetic radiation has a frequen

A particular form of electromagnetic radiation has a frequency of 9.87x10^15Hz. a)What is it\'s wavelength in nanometers? b)in meters? c)what region of the electromagnetic spectrum would you assign it? d)what is the energy (in joules) of one quantum of this radiation?

Solution

Sol)

a) We know that f = c / w
Where
c = speed of light = 3 * 10⁸ m/s
w = wave length = ?
f = frequency = 9.87*10¹⁵ Hz
Plug the values we get w = c / f
= 0.3039*10^-7 m
= 30.39*10^-9 m
wavelength= 30.39 nm (Since  1 nm = 10^-9 m)

b) wavelength =30.39*10^-9 m

d) The energy E is found from the frequency f by Planck\'s equation: E = hf,
where h is Planck\'s constant, equal to 6.625 * 10^-34 joule-second.

If f=9.87x10¹⁵ Hz
E = (6.625 * 10^-34) *(9.87x10¹⁵⁾ Hz
E=65.388*10^-19 joules