Planck's Law MCQ Quiz - Objective Question with Answer for Planck's Law - Download Free PDF

Explanation:

Thermal Radiation and Its Mechanism

• Thermal radiation is a mode of heat transfer that occurs through the emission of electromagnetic waves, primarily in the infrared spectrum, but it can also include visible light and other wavelengths. This form of energy transfer does not require a medium, meaning it can occur in a vacuum. The energy is emitted by all bodies that have a temperature above absolute zero, due to the thermal vibrations of their molecules and atoms. The amount and nature of the radiation depend on the temperature and the surface properties of the body.

Radiation as a heat transfer mechanism is governed by Stefan-Boltzmann’s law, which states:

Q = σ × A × T⁴

Where:

• Q = Heat transfer via radiation (W)
• σ = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴)
• A = Surface area of the body (m²)
• T = Absolute temperature of the body (K)

Thermal radiation is characterized by the following:

• Electromagnetic Waves: It is the primary mechanism by which thermal radiation occurs. These waves can travel through a vacuum, making radiation the dominant form of heat transfer in outer space.
• Emissivity: The ability of a material to emit energy as thermal radiation is determined by its emissivity, which ranges from 0 (perfect reflector) to 1 (perfect emitter or blackbody).
• Temperature Dependence: The intensity and wavelength distribution of the emitted radiation depend on the temperature of the object.

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

Concept:

Using Planck's distribution law to calculate spectral blackbody emissive power at  wavelength λ 

Calculation:

Given:

T = 800 K , D = 20 cm, λ = 3 μm, 3.743 × 108 W-μm4/m2 and C2 = 1.4387 × 104 μm.K

Using Planck's distribution law to calculate spectral blackbody emissive power at a wavelength of 3 μm.

E_bλ = 3848.42 W/m². μm

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

•  Electrons can jump from one energy level to another, but they can never have orbits with energies other than the allowed energy levels.
• The difference of energy E between the higher energy E₂ and the lower energy state E₁ given by:      

​E_g = hc/λ  

Where E_g is the energy of photon (in eV)

h is Planck's constant (4.14 × 10^-15 eV /s)

c is the speed of the light ( 3 × 10⁸ m/s)

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

Concept:

Planck’s constant: It is a physical constant that is the quantum of electromagnetic action. It relates the energy carried by a photon to its frequency by, E = hν.

Hence, the unit of Planck's constant is    

The unit of Planck's constant is Joule⋅sec and it value is 6.6 × 10^-34 Js.

Where, 

E = energy, 

ν = frequency

h = Planck’s constant.

Explanation:

From the above explanation, we can see that, Planck's constant is a fundament constant used to define quantum energy.

And its value is approximately 6.6 × 10-34 Js.

Hence option 3 is correct among all

•  Electrons can jump from one energy level to another, but they can never have orbits with energies other than the allowed energy levels.
• The difference of energy E between the higher energy E₂ and the lower energy state E₁ given by:      

​E_g = hc/λ  

Where E_g is the energy of photon (in eV)

h is Planck's constant (4.14 × 10^-15 eV /s)

c is the speed of the light ( 3 × 10⁸ m/s)

Concept:

Planck’s constant: It is a physical constant that is the quantum of electromagnetic action. It relates the energy carried by a photon to its frequency by, E = hν.

Hence, the unit of Planck's constant is    

The unit of Planck's constant is Joule⋅sec and it value is 6.6 × 10^-34 Js.

Where, 

E = energy, 

ν = frequency

h = Planck’s constant.

Explanation:

From the above explanation, we can see that, Planck's constant is a fundament constant used to define quantum energy.

And its value is approximately 6.6 × 10-34 Js.

Hence option 3 is correct among all

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

Concept:

Planck’s constant: It is a physical constant that is the quantum of electromagnetic action. It relates the energy carried by a photon to its frequency by, E = hν.

Hence, the unit of Planck's constant is    

The unit of Planck's constant is Joule⋅sec and it value is 6.6 × 10^-34 Js.

Where, 

E = energy, 

ν = frequency

h = Planck’s constant.

Explanation:

From the above explanation, we can see that, Planck's constant is a fundament constant used to define quantum energy.

And its value is approximately 6.6 × 10-34 Js.

Hence option 3 is correct among all

Concept:

Using Planck's distribution law to calculate spectral blackbody emissive power at  wavelength λ 

Calculation:

Given:

T = 800 K , D = 20 cm, λ = 3 μm, 3.743 × 108 W-μm4/m2 and C2 = 1.4387 × 104 μm.K

Using Planck's distribution law to calculate spectral blackbody emissive power at a wavelength of 3 μm.

E_bλ = 3848.42 W/m². μm

Explanation:

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.

Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

Energy per unit volume per unit frequency:

So Planck’s distribution function:

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.