Wien's Displacement Law

Q. A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.01R$. The time period of the second satellite is larger than that of the first one by approximately

1. $0.5\%$
2. $1.5\%$
3. $1\%$
4. $3\%$

Q. A black body has maximum wavelength ${\lambda }_m$ at $2000\text{K}$. Its corresponding wavelength at $3000\text{K}$ will be

1. $\frac{3}{2}{\lambda }_m$
2. $\frac{2}{3}{\lambda }_m$
3. $\frac{16}{81}{\lambda }_m$
4. $\frac{81}{16}{\lambda }_m$

Q. The power radiated by a black body is $P_0$, and the wavelength corresponding to maximum energy is ${\lambda }_0$. On changing the temperature of black body, it was observed that the power radiated becomes $\frac{256}{81}{P}_0$. The shift in wavelength corresponding to the maximum energy will be

1. $\frac{{\lambda }_0}{2}$
2. $\frac{{\lambda }_0}{4}$
3. ${\lambda }_0$
4. $2{\lambda }_0$

Q. A black body is at rest at a temperature of $2880\text{K}$. The energy of radiation emitted by this object with wavelength between $499\text{n-m}$ and $500\text{n-m}$ is $U_1$, between $999$ and $1000\text{nm}$ is $U_2$ and between $1499\text{nm}$ and $1500\text{nm}$ is $U_3$. The Wien's constant $b=2.88\times {10}^6\text{nm-K}$. Then

1. $U_1=0$
2. $U_3=0$
3. $U_1>U_2$
4. $U_2>U_1$

Q. Two metal spheres of the same material have radii $r$ and $2r$ and they emit thermal radiation with maximum intensities at wavelengths $\lambda$ and $2\lambda$ respectively. The respective ratio of the radiant energy emitted by them per second will be

1. $4:1$
2. $1:4$
3. $8:1$
4. $1:8$

Q. A glass flask of volume $200{\text{cm}}^3$ is just filled with mercury at ${20}^{\circ }\text{C}$. The amount of mercury that will overflow when the temperature of the system is raised to ${100}^{\circ }\text{C}$ is

$({\gamma }_{\text{glass}}=1.2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1},{\gamma }_{\text{mercury}}=1.8\times {10}^{-4}{}^{\circ }{\text{C}}^{-1})$

1. $2.15{\text{cm}}^3$
2. $2.69{\text{cm}}^3$
3. $2.52{\text{cm}}^3$
4. $2.25{\text{cm}}^3$

Q. Solar radiation emitted by sun resembles to that emitted by a black body at a temperature of $6000\text{K}$. Maximum intensity is emitted at a wavelength of about $4800\AA$. If the sun is cooled down from $6000\text{K}$ to $3000\text{K}$, then the peak intensity would occur at a wavelength of

1. $4800\AA$
2. $9600\AA$
3. $2400\AA$
4. $19200\AA$

Q.

One nanometre is equal to what?

Q. The intensity of radiation emitted by the sun has its maximum value at a wavelength $510\text{nm}$ and that emitted by another star has the maximum value at $350\text{nm}$. If we treat them as black bodies, then the ratio of the surface temperature of the sun and the star is

1. $0.69$
2. $1.46$
3. $1.21$
4. $0.83$

Q. The adjoining diagram shows the spectral energy density distribution $E_{\lambda }$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16:1$, the value of temperature $T$ is

1. $16000\text{K}$
2. $32000\text{K}$
3. $8000\text{K}$
4. $4000\text{K}$

Q. A satellite is launched into a circular orbit of radius $R$ around earth, while a second satellite is launched into a circular orbit of radius $1.02R$. The percentage difference in the time periods of the two satellites is :

1. $3.0$
2. $2.0$
3. $0.7$
4. $1.5$

Q. The plots for intensity versus wavelength for three black bodies at temperatures $T_1,T_2,T_3$ respectively are shown in figure. Their temperatures are such that

1. $T_1>T_2>T_3$
2. $T_1>T_3>T_2$
3. $T_2>T_3>T_1$
4. $T_3>T_2>T_1$

Q. Which of the following graphs correctly represents the variation of $\log {\lambda }_m$ with $\log T$?
[${\lambda }_m$ is the wavelength corresponding to maximum intensity of radiation and $T$ represents absolute temperature.]

1. 
2. 
3. 
4. 

Q. Why does a piece of red glass when heated and taken out glow with green light?

Q.

What are the two laws of thermal radiation?

Q.

Statement 1 : Radiations of longer wavelengths are predominant at lower temperature.

Statement 2 : The wavelength corresponding to maximum emission of radiations shifts from longer wavelength to shorter wavelength as the temperature increases.

1. Statement 1 is false, statement 2 is true
2. Both Statement 1 and statement 2 are true
3. Statement 1 is true, statement 2 is false
4. Both Statement 1 and statement 2 are false

Q. states that radiation curve for different temperatures peak at different wavelengths that are inversely proportional to the temperature.

1. Wien's law
2. Stefan Boltzmann law
3. Kirchoff's law

Q. Distribution of intensity of emitted energy as a function of wavelength is shown in the figure. Point $A$ corresponds to the peak wavelength emitted by a body at certain temperature. Find the correct option when the temperature of the body increases.

1. Intensity of $A$ increases, wavelength decreases
2. Intensity of $A$ decreases, wavelength decreases
3. Intensity of $A$ increases, wavelength increases
4. Intensity of $A$ decreases, wavelength increases

Q.

What are the different types of radiation?

Q. A tunnel has been dug through the centre of the earth, and a ball is released in it. It executes S.H.M. with time period

1. $42\text{minutes}$
2. $1\text{day}$
3. $1\text{hour}$
4. $84.6\text{minutes}$

Q. 100 Watt of bulb is emitting monochromatic light having wavelength 6000 A^°. calculate the photon emitted by bulb. (1) per second (2) 5 minute time

Q. Mass $m$ of a liquid $\text{A}$ is kept in a cup at a temperature of ${90}^{\circ }\text{C}$. When placed in a room having temperature of ${20}^{\circ }\text{C}$, it takes $5\text{min}$ for the temperature of the liquid to drop to ${30}^{\circ }\text{C}$. Another liquid $\text{B}$ having nearly the same density as $\text{A}$ and of mass $m$, kept in another identical cup at ${50}^{\circ }\text{C}$ takes $5\text{min}$ for its temperature to fall to ${30}^{\circ }\text{C}$ when placed in a room having temperature ${20}^{\circ }\text{C}$. If the two liquids at ${90}^{\circ }\text{C}$ and ${50}^{\circ }\text{C}$ are mixed in a calorimeter where no heat is allowed to leak, find the final temperature of the mixture. Assume that Newton's law of cooling is applicable for the given temperature ranges.

1. ${72}^{\circ }\text{C}$
2. ${69.7}^{\circ }\text{C}$
3. ${66}^{\circ }\text{C}$
4. ${52}^{\circ }\text{C}$

Q. The plots for intensity versus wavelength for three black bodies at temperatures $T_1,T_2,T_3$ respectively are shown in figure. Their temperatures are such that

1. $T_1>T_2>T_3$
2. $T_1>T_3>T_2$
3. $T_2>T_3>T_1$
4. $T_3>T_2>T_1$

Q. Upon increasing the temperature of a black body, it is observed that the wavelength corresponding to maximum energy changes from $0.26\mu \text{m}$ to $0.13\mu \text{m}$. The ratio of the emissive powers of the body at the two temperatures is:

1. $\frac{16}{1}$
2. $\frac{4}{1}$
3. $\frac{1}{16}$
4. $\frac{1}{4}$

Q.

Experimental investigations show that the intensity of solar radiation is maximum for a wavelength $480nm$ in the visible region. Estimate the surface temperature of the sun. Given Wien's constant, $b=2.88\times {10}^{-3}mK$.

1. 5000 K

2. 6000 K

3. 8000 K

4. ${10}^{6}K$

Q. Thermal radiations are electromagnetic waves belonging to

1. visible region
2. infrared region
3. ultraviolet region
4. All of the above

Q. The work function of a metal is $3.0eV$, then which of the following can cause photoelectric emission?

1. $414nm$
2. $300nm$
3. $200nm$
4. all of the above

Q.

What is the wavelength of the range of electromagnetic waves?

Q. We are not able to feel the radiation pressure of sunlight because -

1. it is incident along the body surface.
2. our skin is insensitive to it.
3. its magnitude is very small.
4. None of these

Q.

A certain electromagnetic wave has a wavelength of$625nm$. What region of the electromagnetic spectrum is it found?