Black body radiation and Wien displacement law questions

Black Body Radiation

A black body is an object that totally absorbs all of the light that it collects, and reflects none. A black body is also a perfect emitter of light over all wavelengths. Black Body radiation is basically a system that absorbs all the radiation happening or incident on it and releases or radiates the energy which is characteristic of this radiating system only, without depending upon the radiation type incident on it. It is also known as cavity radiation.

With a temperature above absolute zero, every object emits electromagnetic (EM) radiation nearly over all wavelengths. This happens because of the random motions of tiny particles, atoms and molecules present in the object, which defines the object’s temperature.

The amount of radiation released at each wavelength does not hang on any other property of the object; it only depends on the object’s temperature. This was mathematically defined by German physicist Max Planck. This phenomenon is usually referred to as thermal radiation by scientists. Alternatively, the term ‘black body’ radiation is also used by them.

The following laws explains the characteristics of Black Body radiation-:

Wien’s Law Formula

Wien’s Law Formula

λmax=b/T

  • T is the temperature in kelvins
  • b is the Wien’s displacement constant = 2.8977*103 m.K

Planck’s Law Formula

Planck’s law

Eλ=8πhc/λ5(hc/eπKT−1)

  • Eλ is the wavelength
  • T is the absolute temperature

Stefan-Boltzmann Law Formula

Stefan-Boltzmann Law

E ∝ T4

  • E is the total energy emitted
  • T is the absolute temperature

What is Wien’s Law?

Named after the German Physicist Wilhelm Wien, Wien’s law says that objects of different temperatures release spectra that peak at different wavelengths. Hotter objects appear blue because they emit radiations of shorter wavelengths. Likewise, cooler objects appear reddish because they emit radiation of longer wavelengths.

Therefore, in 1893, Wien’s law or Wien’s law of displacement was derived, which states that at wavelengths that are inversely proportional to temperatures, the black body radiation has different temperature peaks.

Mathematical representation of the law:

λmax = b/T

Where,

b denotes Wien’s displacement constant = 2.8977*103 m.K

T denotes the temperature in kelvins

Wien’s displacement constant: b

Wien’s constant is a physical constant that expresses the relation between the thermodynamic temperature and the wavelength of a black body. It is a product of the temperature and wavelength of the black body, which becomes shorter as the wavelength ranges maximum with temperature.

Important Questions on Black body Radiations and Wein Displacement Law

1) The relationship at which maximum value of monochromatic emissive power occurs, that is, the relation between the wavelength and temperature of a black body, (Wavelength) MAX T = constant is termed as

a) Planck’s law

b) Wein’s law

c) Lambert’s law

d) Kirchhoff’s law

Correct Option: (b)

Explanation: The answer will be Wien’s law because from the spectral distribution of black body emissive power, it is apparent that the wavelength related with a maximum rate of emission depends upon the absolute temperature of the radiating surface.

2) A body initially at 600 K cools down by radiating heat to the ambient atmosphere maintained at 400 K. When the body has cooled to 500 K, the cooling rate as a percentage of original rate is about

a) 30.1

b) 45.5

c) 56.3

d) 87.4

Correct Option: (a)

Explanation: Q2/Q1 = (500)4 – (400)4/ (600)4 – (300)4 = 30.1

3) The total emissive power of a small body is 4.5 kW/m2. What will be its surface temperature of maximum emission?

a) 345.65 K

b) 530.77 K

c) 236.54 K

d) 367.82 K

Correct Option: (b)

Explanation: E = σ T4. So, T = 530.77 K.

4) Four similar pieces of copper were heated at the same temperature and then left in the environment to cool. Also, these pieces were painted with different colours of paints. Which among the following paints will give fast cooling?

a) White

b) Black

c) Rough

d) Yellow

Correct Option: (b)

Explanation: The black paint has the highest emissivity that is, unity. Thus, when painted black the emitted radiant energy will be maximum.

5) As the wavelength of the radiation declines, the strength of the black body radiations_____

a) Increases

b) Decreases

c) First decreases then increases

d) First increases then decreases

Correct Option: (d)

Explanation: As the body gets hotter in the case of black body radiation, the wavelength of the emitted radiation decreases. Though, the intensity up to a particular wavelength first increases and then starts decreasing.

6) The phenomenon in which hot bodies emit radiation is known as?

a) X-rays

b) Black-body radiation

c) Visible light

d) Gamma radiations

Correct Option: (b)

Explanation: Max Planck gave the phenomenon of black body radiations. He stated that over a wide range of wavelengths hot bodies emit radiation. Radiation of all frequencies are released and absorbed by an ideal body. Such a body is called a Black Body, and the radiations produced by it are called Black body radiations.

7) What relation between absorptive power, emissivity, and e is given by Kirchhoff’s law?

a) e < a

b) e = a

c) e > a

d) no specific relation

Correct Option: (b)

Explanation: According to Kirchhoff’s law, for any object the absorptive power is always equal to emissivity. Both of them are equal to one for a black body.

8) The unit of absorptive power is?

a) T

b) Ts-1

c) Ts2

d) No unit

Correct Option: (d)

Explanation: Absorptive power is the ratio of energy absorbed per unit area upon energy incident per unit time per unit area. Therefore, absorptive power will be unity for a black body.

9) Which among the following colours indicates that the iron rod is at the lowest temperature, when it is heated and the colours at different temperatures are noted?

a) Red

b) White

c) Orange

d) Blue

Correct Option: (a)

Explanation: The frequency of the released radiation continues to increase as the body gets hotter. Out of any colour, blue colour has the highest frequency. Therefore, as the iron rod gets heated it becomes red first, then orange, white and finally to blue colour.

10) A black body may not be a perfect emitter of radiations but it’s a perfect absorber of radiations.

a) False

b) True

Correct Option: (a)

Explanation: A black body absorbs all the radiations falling on it and would release all of them when heated, as the definition says. Therefore, the above statement is false.

Practice Questions

  1. What are the examples of Wien’s displacement law?
  2. What are the characteristics of Black Body radiations?
  3. Define Wien’s constant.
  4. What is Black Body radiation?
  5. Who derived the expression for Black Body radiation?

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