Estimate the peak wavelength for radiation from the following sources, assuming

Question

Estimate the peak wavelength for radiation from the following sources, assuming blackbody emission.

(a) the universe at T = 2.725 K cm

(b) a floodlamp at 2800 K nm

(c) ice at -1°C µm

(d) helium at 4 K mm

In what region of the EM spectrum is each?

microwave, infrared, near infrared, and far infrared respectively

infrared, near infrared, far infrared, and microwave respectively

far infrared, microwave, infrared, and near infrared respectively

microwave, infrared, far infrared, and near infrared respectively

infrared, far infrared, near infrared, and microwave respectively

near infrared, microwave, infrared, and far infrared respectively

Explanation / Answer

We can calculate the wavelength of the radiation emitted by various sources by using Wien’s displacement law

It relates the absolute temperature of a body and the wavelength of the radiation emitted by it.

It states that product of the wavelength of the corresponding radiation with maximum intensity and absolute temperature of the object is constant

Let the wavelength be and temperature be T

Wien’s displacement law is given by * T = b

Where b = 2.89 * 10-3 m – K is called Wien’s constant

i)wavelength of the radiation emitted by universe

Temperature of the universe is T = 2.725 K

                     * T = 2.89 * 10-3

                              = 2.89 * 10-3 / 2.725

                              = 1.06055 * 10-3 m

                              = 0.106055 cm

Which falls into microwave region

ii)Wavelength of the radiation emitted by flood lamp

Temperature of the flood lamp T = 2800 K

Now       * T   = 2.89 * 10-3

                       = 2.89 * 10-3 / T

                         = 2.89 * 10-3 / 2800

                         = 0.00103 * 10-3 m

                         = 1030 nm

Which falls into infrared region

iii)wavelength of the radiation emitted by ice

Temperature of the ice is T = - 1 0 C = 272 K

Now         * T = 2.89 * 10-3

                     = 2.89 * 10-3 / T

                         = 2.89 * 10-3 / 272

                         = 0.01063 * 10-3 m

                         = 10.63 µ m

Which falls into near infrared region

iv)wavelength of the radiation emitted by helium

Temperature of the He is given by T = 4 K

Now               = 2.89 * 10-3 / T

                        = 2.89 * 10-3 / 4

                        = 0.7225 * 10-3 m

                      = 0.7225 mm

Which falls into far infrared region

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