Quiz on Wien displacement law-Jayam chemistry learners

 MCQs with answers on Wien displacement law 

Introduction

Wien displacement law is a mathematical approach to measure the highest wavelength of blackbody emission with maximum intensity at a fixed temperature of T. It clarifies the peak wavelength movement to shorter wavelengths at higher temperatures of heated objects. The law especially held good at shorter wavelengths of radiation emissions. And it failed to measure the peak wavelength positions of blackbody curves at higher wavelengths in constant temperature conditions. It plays a significant role in the color identification of thermal objects. This blog post not only discusses MCQs with answers on Wien displacement law, but it also includes image-rich topic supplements such as an infographic & mind map of Wien displacement law. 

Wilhelm Wein, in 1893, derived a formula to measure the highest spectral radiance of a blackbody as a function of its wavelength at a particular temperature and is renowned as Wien displacement law. Here is the Wien displacement law formula;

λ_m x T = b

λ_m denotes the wavelength of thermal radiation with peak intensity.

T= absolute temperature of the body.

b=Wien's constant.

Table of contents:

Multiple choice questions and answers on Wien displacement law

Answer whether the following statement is true or false

Reasoning questions and answers on Wien displacement law

An infographic on Wien displacement law

Mind map of Wien displacement law

Difference between Wien’s constant and Planck’s constant

Match the following table

Multiple choice questions and answers on Wien displacement law:

1. Wien displacement law applies to _______________

1. Uniform rigid solids
2. Hot objects
3. Isolated cooled bodies
4. Celestial objects

Answer:
Hot objects
Explanation:
Wien displacement law measures the spectral line intensities of blackbody emissions at shorter radiation wavelengths. Hence, it applies to hot objects resembling the black body.

2. What is the Wien displacement law formula?

1. λ_mXT = b
2. λ_mxb = T
3. bxT = λ_m
4. λ_m = T/b

Answer:
λ_mxT = b
Explanation:
Wien displacement formula shows the inversely proportional relationship between the maximum intense wavelengths of emitted blackbody radiations with their absolute temperature. And their product is equal to a fixed numerical value called Wien's constant.

3. Wien displacement formula results differ from blackbody curves at___________

1. Longer frequencies
2. Lower temperatures
3. Longer wavelengths
4. Higher temperatures

Answer:
Longer wavelengths
Explanation:
Wien displacement law measures the spectral brightness of emitted thermal electromagnetic radiations. And it gives accurate results at shorter wavelengths. But it fails to show the exact outcomes at longer radiation wavelengths due to the consideration of light as a wave.

4. What is the essence of Wien displacement law?

1. λ_m decreases at higher temperatures of blackbody emissions
2. λ_m increases with blackbody's temperature
3. λ_m decreases at lower temperatures of blackbody radiation
4. λ_m is higher toward longer wavelengths of blackbody emissions

Answer:
λ_m decreases at higher temperatures of blackbody emissions
Explanation:
Wien displacement law is an empirical generalization to measure the peak intense wavelengths at above zero kelvin temperature of the object. Moreover, λ_m and T both vary inversely. Hence, the λ_m value declines at higher temperatures of released blackbody radiations.

5. What is the value of Wien's constant in the CGS units?

1. 0.289 cm Kelvin
2. 28.9 cm Kelvin
3. 2.89 cm Kelvin
4. 2890 cm Kelvin

Answer:
0.289 cm Kelvin
Explanation:
Wien's constant shows the proportionality relationship between the high intense wavelength and absolute temperature. And this specific numerical quantity's value in the CGS system is 0.289 centimeter Kelvin.

6. What is the SI unit of temperature?

1. Degree Celsius
2. Celsius
3. Centigrade
4. Kelvin

Answer:
Kelvin
Explanation:
Kelvin is the primary unit of temperature in the SI system.

7. When the blackbody's temperature increases, what happens to a frequency corresponding to the maximum intensity?

1. Increases
2. Decreases
3. Both 1 and 2
4. Remains constant

Answer:
Increases
Explanation:
When the blackbody's enclosure temperature increases, expelled thermal electromagnetic radiation frequency rises. It happens due to the directly varying relationship between the energy and frequency of light.

8. When was Wien displacement law invented?

1. 1809
2. 1893
3. 1906
4. 1890

Answer:
1893
Explanation:
Wilhelm Wein, in 1893, discovered a mathematical relationship to enumerate the peak intense wavelengths of ejected blackbody emissions at various temperatures on the Kelvin scale. And it was renowned as the Wien displacement law formula.

9. Variation of blackbody radiation intensity with temperature conditions is _____________

1. Uniform
2. Non-uniform
3. Remains constant
4. Unsure

Answer:
Non-uniform
Explanation:
In general, blackbody radiation emission is dependent on the body's temperature. So, a body's emissive power is directly proportional to its temperature. Hence, the released blackbody radiation intensity is non-uniform at temperature fluctuations.

10. The wavelength of maximum intensity moves towards______________________at higher temperatures

1. Shorter wavelengths
2. Longer wavelengths
3. Longer emissivity
4. Lower frequencies

Answer:
Shorter wavelengths
Explanation:
Wien's law exhibits the displacement of the most intensified wavelength (λm) towards the left (i.e., shorter wavelength side) in the blackbody graph. It implies the quantum size of blackbody emissions increases at higher temperatures. Hence, the intense wavelength peak position moves ahead.

11. What is the SI unit of Wien's constant for intense frequency peak?

1. sec^-1 Kelvin
2. sec/Kelvin
3. Hertz/Kelvin
4. Meter Hertz

Answer:
Hertz/Kelvin
Explanation:
The SI unit of frequency is Hertz, and the temperature is Kelvin. Wien's constant is the ratio of emitted radiation frequency and temperature. Hence, its SI unit is Hertz/Kelvin.

12. Which region of the electromagnetic spectrum does the emitted blackbody radiation belong to at 25 degrees centigrade temperature?

1. Ultraviolet region
2. Visible region
3. Infrared region
4. Cosmic region

Answer:
Infrared region
Explanation:
By Wien displacement law, 25 degrees centigrade gives a maximum intense wavelength peak at 9.6 micrometers. It falls in the far infrared region of the electromagnetic spectrum.

13. Wien displacement law is a special case of __________________law

1. Rayleigh-Jeans law
2. Planck law
3. Kirchhoff's law
4. Prevost's law

Answer:
Planck law
Explanation:
The Wien displacement formula works well at shorter wavelengths of blackbody radiations. But, the Planck quantum formula applies to all frequencies and temperature conditions of thermal electromagnetic emissions. Hence, the Wien law is a remarkable case of Planck law.

14. Which of the following law helps to determine the color of stars based on their temperature?

1. Wien displacement law
2. Kirchhoff's law
3. Rayleigh-Jeans law
4. Stefan-Boltzmann law

Answer:
Wien displacement law
Explanation:
The Wien displacement law measures the topmost intense wavelength position in the blackbody curve at a particular temperature. Hence, it tells the color of hot objects emitting thermal electromagnetic radiation, including stars.

15. What is the Wien displacement formula for intense frequency crests?

1. ν_mxT = b
2. ν_m = bxT
3. T = ν_mxb
4. ν_mxb = T

Answer:
ν_m = bxT
Explanation:
The Wien displacement formula shows the directly proportional relationship between the most intense frequency position and the body's absolute temperature.

Answer whether the following statement is true or false:

1. Wien displacement law shows that the wavelength of emitted radiation decreases at higher temperatures.

A. True

B. False

Answer:

False

Explanation:

Wien displacement law exhibits the inversely proportional relationship between intense wavelength position and the body's absolute temperature. As a result, λ_m decreases at higher temperatures.

2. Absolute temperature is the lowest possible temperature that a body can attain.

A. True

B. False

Answer:

True

Explanation:

The oscillating charged particles of a substance possess minimum kinetic energy at absolute zero temperature. Hence, absolute zero temperature is the lowest attainable temperature state of the body.

3. Wien's constant is a universal constant.

A. True

B. False

Answer:

False

Explanation:

Wien's constant (b) is a proportionality constant. Its value is different for λ_m and ν_m calculations. Consequently, its value is not persistent with time. And it is not a universal constant.

4. The symbol λ_m denotes both the intensity and maximum wavelength of released blackbody radiations.

A. True

B. False

Answer:

False

Explanation:

λ_m designates the maximum wavelength of emitted thermal electromagnetic radiation with high intensity. But not both the wavelength and intensity of radiation.

5. Wien displacement law applies to all terrestrial objects.

A. True

B. False

Answer:

False

Explanation:

Wien displacement law applies to hot objects which can release blackbody radiations. But it does not apply to cold substances capable of releasing electromagnetic radiations due to electron transitions.

Reasoning questions and answers on Wien displacement law:

Read the assertion and explanation statements carefully. And pick the correct option from the following. The options are common to all questions.

A. Both assertion and explanation are correct

B. Assertion is true. And the explanation is false

C. Assertion is false. And the explanation is correct.

D. Both assertion and explanation are false.

Question-1:

Assertion:

Wien displacement law helps to measure the wavelengths of spectral lines in atomic spectra.

Explanation:

It shows the inversely proportional relationship between λm and the body's temperature on the Kelvin scale.

Answer:

The assertion is false. And the explanation is correct.

Clarification:

Wien displacement law does not calculate the wavelengths of emitted spectral lines. Instead, it measures the topmost wavelength position of released light with maximum intensity at a particular temperature of T.

Question-2:

Assertion:

The product of λm and T is always constant.

Explanation:

2.89 x 10^-3 mK is the value of λm x T.

Answer:

Both the assertion and explanation are correct.

Clarification:

The product of λm and T is equal to a fixed numerical quantity called Wien's constant. And the value of b in the SI system is 2.89 x 10^-3 mK.

Question-3:

Assertion:

At higher temperatures, the peak of the blackbody curve escalates.

Explanation:

λm increases at higher temperatures following Wien's law.

Answer:

The assertion is true. And the explanation is false.

Clarification:

The growing blackbody curve's λm position at the higher temperature suggests that the emissive power of blackbody emissions increases with temperature. But the wavelength of the most intense blackbody emission decreases with the temperature rise.

Question-4:

Assertion:

Wien displacement law fails at longer wavelengths of thermal electromagnetic emissions.

Explanation:

It is due to the inversely proportional relationship between λm and temperature of Wien's formula.

Answer:

The assertion is true. And the explanation is false.

Clarification:

Wien displacement law fails at longer wavelengths of blackbody radiations due to consideration of the wave character of light. But not due to λm and temperature relationship in the Wien displacement law formula.

Question-5:

Assertion:

Wien displacement law helps to identify the color of emitted hot electromagnetic radiations.

Explanation:

All blackbody radiations exhibit color at shorter wavelengths.

Answer:

The assertion is correct. But the explanation is false.

Clarification:

Electromagnetic radiations with wavelengths between 350 to 700 nm lie in the visible region and show the color that a human eye can perceive. The Wien displacement formula aids in calculating the maximum intense wavelengths of emitted blackbody radiation and determines their exhibited color.

Question-6:

Assertion:

Wien displacement law is a remarkable case of Planck quantum law.

Explanation:

Wien displacement law relies on the wave character of light. And Planck's law depicts the particle behavior of light. Hence, both these laws are irrelevant.

Answer:

The assertion is true. And the explanation is false.

Clarification:

Wien displacement law, discovered in 1893, successfully measured λm at shorter radiation wavelengths. Besides, Planck quantum law, invented in 1900, applies to both shorter and longer wavelengths of blackbody emissions. Hence, Wien displacement law is a remarkable case of Planck quantum law.

Question-7:

Assertion:

The Wien displacement graph shows a linearly declining curve for λm and temperature.

Explanation:

It shows the movement of the peak intense wavelength position towards shorter wavelengths.

Answer:

Both the assertion and explanation are correct.

Clarification:

The Wien displacement graph shows the variation between the most intense wavelength and the body's absolute temperature. It is a linearly declining line depicting the shift of λm toward shorter radiation wavelengths.

Question-8:

Assertion:

Following Wien displacement law, white-colored radiation is the hottest blackbody emission of the visible region.

Explanation:

It is due to the reflecting power of white-colored objects.

Answer:

The assertion is correct. And the explanation is false.

Clarification:

At about 12000 degrees centigrade temperature, the blackbody emits white-colored radiation. And a further rise in temperature shifts the wavelengths of thermal electromagnetic emissions to the ultraviolet region. Hence, white-colored radiation is the hottest blackbody radiation in the visible zone of the blackbody spectrum.

Question-9:

Assertion:

b is a fixed numerical quantity used in the Wien displacement formula.

Explanation:

Derivation of Wien's constant value involves other physical quantities such as Planck's constant (h) and Boltzmann's constant (k).

Answer:

Both the assertion and explanation are correct.

Clarification:

b is a constant arithmetic value that involves the following derivation method from other physical quantities, such as h, c, k, and x.

λ_mxT = b
λ_m = ^b⁄_T
λ_m = ^hc⁄_xkT

It implies Wien’s constant (b) = hc/xk

Where,

h = Planck’s constant. And its value is 6.626 x 10^-34 joule second

c = Velocity of light. And its value is 3 x 10⁸ meter per second

x = a constant. And its value is 4.965

k = Boltzmann constant. And its value is 1.3807 x 10^-23 joules per Kelvin

T = Absolute temperature of the body

By substituting all the values of the physical quantities in the above equation, we get;

λ_m = ^{(6.626 x 10-34) x (3 x 108)}⁄_{4.965 x (1.3807 x 10^-23)}
λ_m = ^{19.878 x 10-26}⁄_{6.855 x 10^-23}
λ_m = 2.899 x 10^-3 meter Kelvin

Question-10:

Assertion:

The human body temperature is approximately 37 degrees centigrade.

Explanation:

We can calculate the wavelength of emitted blackbody radiations of the human body using the Wien displacement formula.

Answer:

Both the assertion and explanation are correct.

Clarification:

Human body temperature (T) = 37 degrees centigrade = 37+273 = 310 Kelvin

Wien’s constant value (b) = 2.89 x 10^-3 meter Kelvin

Following Wien displacement law, we have;

λ_m x T = b

^{λ_m = 2.89 x 10-3 meter Kelvin}⁄_{310 Kelvin}

λ_m = 0.00932 x 10^-3 meter

λ_m = 932 x 10^-8 meter

λ_m = 9.32 μm

An infographic on Wien displacement law:

Wien displacement law is a new formulation for measurement of the crest wavelength position of blackbody curves. A blackbody curve is a graphical representation of the energy distribution of emitted thermal electromagnetic radiations over a wide range of temperatures in thermal equilibrium conditions. Also, it is a plot between emissive power and wavelengths of released blackbody radiations at a particular temperature of T. Moreover, it is a hill-shaped curve with a crest designating λ_m for that temperature range.

The Wien displacement law is a temperature-specific mathematical formula to tell the maximum wavelength of the blackbody emissions that is the most intense. Wilhelm Wein, in 1893, discovered this empirical relation to find out the inversely proportional relationship between λ_m and the body's absolute temperature. Also, Wein inserted an empirical fitting parameter to get precise results from mathematical calculations. And the fixed arithmetic quantity value is equal to 2.89 x 10^-3 mK, known as Wien's constant.

The linearly declining graph for emitted radiation wavelengths and absolute temperature specifies that the most intense wavelength peak shifts toward shorter wavelengths at higher temperatures. Hence, the Wien displacement works best at shorter radiation wavelengths, and it failed to give precise results for longer radiation wavelengths of blackbody emissions. Here is a table illustrating the variation of radiation wavelengths expressed in nanometers with temperature measured in Kelvin. The graph shown in the infographic is drawn based on the data mentioned in the table.

Wavelength in nm	Temperature in Kelvin
350	8257
400	7225
450	6422
550	5255
650	4446
750	3853

Coming to applications of Wien displacement law, it helps to measure the highly intense wavelengths of radiation emissions that play a vital role in designing thermal and medical equipment used for heating purposes.

Mind map of Wien displacement law:

The mind map of the Wien displacement formula discusses both the maximum intense wavelength and frequency peaks formula at absolute body temperature conditions. The λ_m empirical relation elucidates the inversely proportional relationship between wavelength and the body's temperature with the b value 2.89 x 10^-3 mK. Similarly, the peak frequency mathematical rule defines the directly proportional relationship between ν_m and T with the b value 0.058 THz/ K.

In addition to that, it discusses the description, applications, and limitations of Wien displacement law in a simplified manner.

Difference between Wien's constant and Planck's constant:

Wien's constant	Planck's constant
Wien's constant is an empirical fitting parameter in the Wien displacement formula to measure the maximum intense emissions wavelengths or frequencies at the body's absolute temperature conditions.	Planck's constant is an empirical fitting parameter in the Planck quantum formula to measure the magnitude of emitted radiant energies from the frequencies of released blackbody radiations.
It is a fixed numerical quantity showing the proportionality relation of λm and temperature (or) νm and temperature.	It is a constant arithmetic value showing the proportionality relationship between the photon's energy and frequency.
Wilhelm Wein, in 1893 introduced it in the Wien displacement formula.	Max Planck, in 1900 invented it for the Planck quantum formula.
The English alphabet "b" denotes it.	The English alphabet "h" denotes it.
It has two different values. For λm measurement, the value of b = 2.89 x 10-3 mK, and b = 0.058 THz/ K for νm enumerations.	The value of Planck's constant in the SI system is 6.626 x 10-34 joule seconds.
It is not a universal constant that is constant with time.	It is a universal physical quantity.

Match the following table:

Column-A	Column-B
A. Wien displacement law	1. Particle behaviour of light
B. Wien's constant	2. A universal physical quantity
C. Planck's quantum law	3. Light is a wave
D. Linear declining curve	4. A proportionality constant
E. Planck's constant	5. λm shifts toward shorter wavelengths

Answers:

A-3, B-4, C-1, D-5, E-2