### What Is Wiens Law?

Wien’s Law Wein’s law is also known as the Wein’s displacement law, it is named after German Physicist Willhelm Wein in honor of his extraordinary contribution in explaining black body radiations. Wein’s law gives us a relationship between the wavelength of light that corresponds to the highest intensity and the absolute temperature of the object.

### What is Wien’s law in simple terms?

Wien’s Law – Wien’s Displacement Law – Applications – BYJU’S Wien’s Law, named after the German Physicist Wilhelm Wien, tells us that objects of different temperatures emit spectra that peak at different wavelengths. Hotter objects emit radiations of shorter wavelengths, and hence they appear blue.

• Wien’s law or Wien’s displacement law, named after Wilhelm Wien, was derived in the year 1893 which states that has different peaks of temperature at wavelengths that are inversely proportional to temperatures.
• Mathematical representation of the law:
• $$\begin \lambda _ = \frac \end$$

where, b is the Wien’s displacement constant = 2.8977*103 m.K T is the temperature in kelvins Physical constant defining the relationship between the temperature of the black body and the wavelength is known as Wien’s constant. It is a product of the temperature and wavelength of the black body, which grows shorter as the wavelength reaches a maximum with temperature.

• Frequency dependent formula:

$$\begin \upsilon _ = \frac kT\approx (5.879*10^ \frac )T\end$$ where, k is the Boltzmann constant h is the Planck’s constant T is the temperature in kelvin 𝛼 is the equivalent value = 2.821 $$\begin \lambda _ = \frac } \frac =\frac nm.K} \end$$

• Incandescent bulb light: With the decrease in temperature of the filament, wavelengths are longer making light appear redder.
• The temperature of the sun: One can study the peak emission per nanometres of the sun with a wavelength of 500 nm in the green spectrum, which is in the human eye sensitive range.

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### What is Wiens law used for?

Department of Astronomy: Introductory Astronomy Wien’s Law is an important formula that allows us to determine the temperature of a star. It is based on the fact that hotter objects have more energy than cooler objects and therefore emit more radiation at higher frequencies than at lower frequencies.

Wien discovered that there was a direct relationship between the wavelength (or frequency) at which an object emits most of its energy and the temperature of that object. His law is shown above; in this form, wavelength must be measured in Angstroms (one Angstrom is 10^(-10) meters) and temperature in degrees Kelvin.

We can understand the logic of Wien’s law by looking at the following graphs: Notice that as the wavelength where the most energy is given off (maximum wavelength) goes from red to green to blue, the temperature increases. Now, we know that light with longer wavelengths has lower frequencies and therefore less energy than light with shorter wavelengths.

• Since the wavelength of red light is longer than green light (and green light is longer than blue), red light must have a lower frequency and less energy than green light (and green has less energy than blue).
• Therefore, we expect a star that emits mostly blue light to emit more energy (and thus be hotter) than a star that emits mostly red light (if they are the same size).

We see from the graphs that our expectation is correct: the temperature for a star which emits most of its light at a maximum wavelength of 600 nanometers is 5000 K, the temperature for a star with a maximum wavelength at about 500 nanometers is 6000 K, and the temperature for a star with a maximum wavelength at 400 nanometers is about 7000 K.

### When was Wien’s law?

Work – When a completely dark body is heated, it emits visible light and other electromagnetic radiation. The spectrum of the radiation is entirely dependent on the temperature of the body and not its composition. In 1893 Wilhelm Wien formulated his displacement law, which indicates at which wavelength the radiation is most intense at a certain temperature.

#### What does Wien’s law reveal?

SUMMARY Visible light is a particular type of electromagnetic radiation and travels through space in the form of a wave. A wave is characterized by the wave period, the length of time taken for one complete cycle; the wavelength, the distance between successive wave crests; and the wave amplitude, which measures the size of the disturbance associated with the wave.

The wave frequency is simply 1 divided by the wave period—it counts the number of wave crests that pass a given point in one second. Diffraction is the tendency of a wave to spread out after passing through an opening or to bend around a corner. Interference is the ability of two waves to reinforce or partially cancel each other.

Electrons and protons are elementary particles that carry equal and opposite electrical charges. Any electrically charged object is surrounded by an electric field that determines the force it exerts on other charged objects. Like gravitational fields, electric fields decrease as the square of the distance from their source.

When a charged particle moves, information about that motion is transmitted throughout the universe by the particle’s changing electric field. The information travels in the form of a wave at the speed of light. Both electric and magnetic fields are involved, so the phenomenon is known as electromagnetism.

A beam of white light is bent, or refracted, as it passes through a prism. Different frequencies of light within the beam are refracted by different amounts, so the beam is split up into its component colors—the visible spectrum. The color of visible light is simply a measure of its wavelength—red light has a longer wavelength than blue light.

The entire electromagnetic spectrum consists of (in order of increasing frequency) radio waves, infrared radiation, visible light, ultraviolet radiation, X rays, and gamma rays. The opacity of Earth’s atmosphere—the extent to which it absorbs radiation—varies greatly with wavelength. Only radio waves, some infrared wavelengths, and visible light can penetrate the atmosphere and reach the ground from space.

The temperature of an object is a measure of the speed with which its constituent particles move. The intensity of radiation of different frequencies emitted by a hot object has a characteristic distribution, called a blackbody curve, that depends only on the temperature of the object.

1. Wien’s law tells us that the wavelength at which the object radiates most energy is inversely proportional to its temperature.
2. Stefan’s law states that the total amount of energy radiated is proportional to the fourth power of the temperature.
3. Our perception of the wavelength of a beam of light can be altered by our velocity relative to the source.

This motion-induced change in the observed frequency of a wave is called the Doppler effect. Any net motion away from the source causes a redshift —a shift to lower frequencies—in the received beam. Motion toward the source causes a blueshift, The extent of the shift is directly proportional to the observer’s radial velocity relative to the source.

1. SELF-TEST: TRUE OR FALSE? 1.
2. Light, radio, ultraviolet, and gamma rays are all forms of electromagnetic radiation.2.
3. Sound is a familiar type of electromagnetic wave.3.
4. The amount of diffraction increases with increasing wavelength.4.
5. Interference occurs when one wave is brighter than another; the fainter wave cannot be observed.5.

Electromagnetic waves cannot travel through a perfect vacuum.6. Electromagnetic waves all travel at the same speed, the speed of light.7. Visible light makes up the greatest part of the entire electromagnetic spectrum.8. Ultraviolet light has the shortest wavelength of any electromagnetic wave.9.

A blackbody emits all its radiation at one wavelength or frequency.10. A perfect blackbody emits exactly as much radiation as it absorbs from outside.11. The shape of a blackbody curve depends on the temperature of the body.12. The frequency at which the blackbody curve peaks increases with temperature.13.

Objects moving away from an observer are redshifted because they actually turn red.14. The Doppler effect occurs for all types of wave motion.15. An object emitting radiation, moving transverse to the line of sight, produces no Doppler effect. SELF-TEST: FILL IN THE BLANK 1.

The speed of light is _ km/s.2. The _ of a wave is the distance between any two adjacent wave crests.3. The _ of a wave is measured in units of hertz (Hz).4. _ is the ability of a wave to “bend around corners.” 5. When a charged particle moves, information about this motion is transmitted through space by means of its changing _ and _ fields.6.

The visible spectrum ranges from _ to _ in wavelength.7. Light with a wavelength of 700 nm is perceived to be _ in color.8. Earth’s atmosphere has low opacity for three forms of electromagnetic radiation. They are _, _, and _.9. The peak of an object’s emitted radiation occurs at a frequency or wavelength determined by the object’s _.10.

1. The lowest possible temperature is _ K.11.
2. Water freezes at _ K.12.
3. Because the Sun emits its peak amount of radiation at about 480 nm, its temperature must be about _ K.13.
4. Two identical objects have temperatures of 1000 K and 1200 K, respectively.
5. It is observed that one of the objects emits twice as much radiation as the other.

Which one is it? _.14. If an astronomical object is observed to emit X-rays, it is reasonable to assume its temperature is very _.15. When an observer and/or an object emitting radiation move toward each other, the observer sees the radiation shifted to _ wavelengths.

REVIEW AND DISCUSSION 1. Define the following wave properties: period, wavelength, amplitude, frequency.2. What is the relationship between wavelength, wave frequency, and wave velocity? 3. What is diffraction, and how does it relate to the behavior of light as a wave? 4. What’s so special about c? 5. Compare and contrast the gravitational force with the electric force.6.

Describe the way in which light radiation leaves a star, travels through the vacuum of space, and finally is seen by someone on Earth.7. Name the colors that combine to make white light. What is it about the various colors that causes us to perceive them differently? 8.

What do radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays have in common? How do they differ? 9. In what regions of the electromagnetic spectrum is the atmosphere transparent enough to allow observations from the ground? 10. What is a blackbody? What are the characteristics of the radiation emitted by a blackbody? 11.

What does Wien’s law reveal about stars in the sky? 12. What does Stefan’s law tell us about the radiation emitted by a blackbody? 13. In terms of its blackbody curve, describe what happens as a red-hot glowing coal cools off.14. What is the Doppler effect, and how does it alter the way in which we perceive radiation? 15.

• If Earth were completely blanketed with clouds and we couldn’t see the sky, could we learn about the realm beyond the clouds? What other forms of radiation might be received? PROBLEMS 1.
• A sound wave moving through water has a frequency of 256 Hz and a wavelength of 5.77 m,
• What is the speed of sound in water? 2.

What is the wavelength of a 100-MHz (“FM 100”) radio signal? 3. What would be the frequency of an electromagnetic wave having a wavelength equal to Earth’s diameter? In what part of the electromagnetic spectrum would such a wave lie? 4. According to Wien’s law, how many times hotter is an object whose blackbody emission spectrum peaks in the ultraviolet, at a wavelength of 200 nm, than an object whose spectrum peaks in the red, at 650 nm? According to Stefan’s law, how much more energy does it radiate per unit area per second? 5.

Normal human body temperature is about 37°C, What is this temperature in kelvins ? What is the peak wavelength emitted by a person with this temperature? In what part of the spectrum does this lie? 6. The Sun has a temperature of 5800 K, and its blackbody emission peaks at a wavelength of approximately 550 nm.

At what wavelength does a protostar with a temperature of 1000 K radiate most strongly? 7. Two otherwise identical bodies have temperatures of 300 K and 1500 K, respectively. Which one radiates more energy, and by what factor does its emission exceed the emission of the other body? 8.

1. According to Stefan’s law, how much energy is radiated into space per unit time by each square meter of the Sun’s surface (see More Precisely 3-2)? If the Sun’s radius is 696,000 km, what is the total power output of the Sun? 9.
2. At what radial velocity, and in what direction, would a spacecraft have to be moving for a radio station transmitting at 100 MHz to be picked up by a radio tuned to 99.9 MHz? 10.

Imagine you are observing a spacecraft moving in a circular orbit of radius 100,000 km around a distant planet. You happen to be located in the plane of the spacecraft’s orbit. You find that the spacecraft’s radio signal varies periodically in wavelength between 2.99964 m and 3.00036 m,

## What is Wien’s displacement law Class 11?

• It is an ideal body that absorbs all incident electromagnetic waves or radiation, regardless of the angle of incidence or frequency.
• As it absorbs all colours of light, it is named as black “body”.
• Wien’s displacement law, Planck’s Law and Stefan-Boltzmann laws are the laws that explain the character of a black body.

According to Wien’s Displacement Law, the blackbody radiation curve for different temperature peaks at a wavelength is inversely proportional to the temperature. Planck’s Law states that electromagnetic radiation from heated objects is not released as a continuous form but is made up of discrete quanta or units of energy. Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin! Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz Visit BYJU’S for all Physics related queries and study materials

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View Quiz Answers and Analysis : Blackbody Radiation – Definition, Wien’s Displacement Law, Planck’s Law

## Why Wiens law is called displacement law?

According to Wien’s displacement law λm moves toward the lower part of spectrum and when the temperature decreases, λm gets displaced toward the higher end of the spectrum. This is why it is called Wien’s displacement law.

## What is significance of Wien’s displacement law?

Wien’s displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.

#### What is the formula of Wien’s constant?

Option (D) Formula used: Wien’s constant is given by, b = λ m T where is the peak wavelength of the black body radiation and is the surface temperature of the black body. Wien’s Displacement Law provides the wavelength where the spectral radiance has a maximum value.

## What is the Wien’s displacement law example?

Solved Examples on Wien’s Law – Example 1: The North star emits energy with a wavelength of 410 nm, while the sun emits light at a maximum intensity of 621 nm. What is the ratio of the surface temperatures of the sun and the north star, if these stars behave like black bodies? Answer :

1. We have,
2. λ m T = constant
3. T(S) / T(N) = λ m (N) / λ m (S)
4. T(S) / T(N) = 410 / 621
5. T(S) / T(N) = 0.66

Example 2: Determine the maximum amount of solar radiation using the assumption that the sun’s surface temperature is 5800 K. Where does this value fall on the electromagnetic spectrum? (b = 2.897 × 10 -3 m K). Answer :

• We have,
• λ max = b / T
• λ max = 2.897 × 10 -3 / 5800
• λ max = 4.995 × 10 -7 m
• λ max = 4995 Ă

Example 3: A black body has a wavelength when it is 3510 K in temperature. Its comparable wavelength will be at a temperature of 4100 K. Answer : We have, According to Wien’s displacement law, the black body radiation curve peaks for various temperatures at a wavelength that is inversely proportional to the temperature.

1. λT = constant
2. λ × 3510 = λ’ × 4100
3. λ’ = 3510 / 4100 λ
4. λ’ = 0.85 λ

Example 4: Radiation from stars has a maximal wavelength of 10 -5 m. Identify the star’s rough temperature. Answer :

• We have,
• λ m T = 2.897 × 10 -3
• T = 2.897 × 10 -3 / 10 -5
• T = 2.897 × 10 2 K

Example 5: Consider that the temperature of the earth is 197 K. Analyze the energy that the planet is emitting at its peak wavelength. Answer :

1. We have,
2. λ m T = 2.897 × 10 -3
3. λ m = 2.897 × 10-3 / 197
4. λ m = 0.014 × 10 -3 m

### Who discovered Wien’s displacement law?

There is a simple and interesting relationship between the peak wavelength and the temperature at which a blackbody radiates. Wilhelm Carl Werner Otto Fritz Wien (1864–1928), a Nobel prize recipient in 1911, discovered this behavior of the blackbody, Applying Planck’s law, the spectral radiant emittance at the peak wavelength is Wien’s displacement law. Citation: M. Riedl, Optical Design Fundamentals for Infrared Systems, Second Edition, SPIE Press, Bellingham, WA (2001). View SPIE terms of use. Excerpt from Member: $49.30 Non-Member:$58.00

#### What is Stefan’s law class 11?

Stefan Boltzmann Law – Derivation, Formula, Equation, Examples According to Stefan Boltzmann law, the amount of radiation emitted per unit time from an area A of a black body at absolute temperature T is directly proportional to the fourth power of the temperature.

1. U/A = σT 4,
2. 1) where σ is Stefan’s constant = 5.67 × 10 -8 W/m 2 k 4 A body that is not a black body absorbs and hence emit less radiation, given by equation (1) For such a body, u = e σ AT 4,
3. 2) where e = emissivity (which is equal to absorptive power) which lies between 0 to 1.
4. With the surroundings of temperature T 0, net energy radiated by an area A per unit time.

Δu = u – u o = eσA, (3) ⇒ Also Read

Stefan Boltzmann Law relates the temperature of the blackbody to the amount of power it emits per unit area. The law states that; “The total energy emitted/radiated per unit surface area of a blackbody across all wavelengths per unit time is directly proportional to the fourth power of the black body’s thermodynamic temperature. ”

## What is the Wien’s displacement law example?

Solved Examples on Wien’s Law – Example 1: The North star emits energy with a wavelength of 410 nm, while the sun emits light at a maximum intensity of 621 nm. What is the ratio of the surface temperatures of the sun and the north star, if these stars behave like black bodies? Answer :

1. We have,
2. λ m T = constant
3. T(S) / T(N) = λ m (N) / λ m (S)
4. T(S) / T(N) = 410 / 621
5. T(S) / T(N) = 0.66

Example 2: Determine the maximum amount of solar radiation using the assumption that the sun’s surface temperature is 5800 K. Where does this value fall on the electromagnetic spectrum? (b = 2.897 × 10 -3 m K). Answer :

• We have,
• λ max = b / T
• λ max = 2.897 × 10 -3 / 5800
• λ max = 4.995 × 10 -7 m
• λ max = 4995 Ă

Example 3: A black body has a wavelength when it is 3510 K in temperature. Its comparable wavelength will be at a temperature of 4100 K. Answer : We have, According to Wien’s displacement law, the black body radiation curve peaks for various temperatures at a wavelength that is inversely proportional to the temperature.

1. λT = constant
2. λ × 3510 = λ’ × 4100
3. λ’ = 3510 / 4100 λ
4. λ’ = 0.85 λ

Example 4: Radiation from stars has a maximal wavelength of 10 -5 m. Identify the star’s rough temperature. Answer :

• We have,
• λ m T = 2.897 × 10 -3
• T = 2.897 × 10 -3 / 10 -5
• T = 2.897 × 10 2 K

Example 5: Consider that the temperature of the earth is 197 K. Analyze the energy that the planet is emitting at its peak wavelength. Answer :

1. We have,
2. λ m T = 2.897 × 10 -3
3. λ m = 2.897 × 10-3 / 197
4. λ m = 0.014 × 10 -3 m

## Why Wiens law is called displacement law?

According to Wien’s displacement law λm moves toward the lower part of spectrum and when the temperature decreases, λm gets displaced toward the higher end of the spectrum. This is why it is called Wien’s displacement law.

#### What is Wien’s law quizlet?

-Definition: Wien’s law states that the wavelength at which an object radiates most strongly is inversely proportional to the object’s temperature : The hotter a body is, the more strongly it will radiate at short wavelengths.