Question

# Infrared radiation (heat or thermal energy) spans the electromagnetic spectrum from about 1 to 100 micrometers...

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 )?

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.

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