Question

Infrared radiation (heat or thermal energy) spans the electromagnetic spectrum from about 1 to 100 micrometers (10-6m). What is this range expressed as energy (in Joules)? What is this range expressed as frequency (in s-1 )?

Answer 1

Planck's equation

E = h

Where, E is energy , h is Planck's constant = 6.626*10^-34 J.s

Frequency of radiation ( )=  C/

C is velocity of light = 3*10⁸ m.

is wavelength.

Now, in the given problem

Range of wavelength = 1 to 100 micrometre.

Or, 10^-6 to 10^-4 m.

First part

Now, the energy of wavelength of 10^-6 m

E = 6.626*10^-34 * 3*10⁸/10^-6 = 19.878* 10^-20 Joule.

and energy of wavelength of 10^-4 m is

E = 6.626*10^-34*3*10⁸/10^-4  = 19.878*10^-22 Joule.

Hence, range of energy is

19.878*10^-20 Joule to 19.878*10^-22 Joule.

Second part

Frequency ( for 1 micrometer wavelength)

= 3*10⁸/10^-6 = 3*10¹⁴ s ^-1.

Frequency ( for 100 micrometer wavelength)

= 3*10⁸/10^-4 = 3*10¹² s ^-1.

Hence range of frequency is 3*10¹⁴ to 3*10¹² s ^-1.