Wien's Displacement Law

Q. Thermal radiations are electromagnetic waves belonging to

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

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

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

Q. The energy radiated by a black body at $2300\text{K}$ is found to have maximum intensity at wavelength $1260\text{nm}$, its emissive power being $8000{\text{W/m}}^2$. When the body is cooled to a temperature $T\text{K}$, the emissive power is found to decrease to $500{\text{W/m}}^2$. Find the wavelength at which intensity of emission is maximum at the temperature $T$.

1. $1575\text{nm}$
2. $2520\text{nm}$
3. $1260\text{nm}$
4. $5040\text{nm}$

Q.

According to Wien's displacement law wavelength corresponding to maximum intensity decreases when the temperature of blackbody increases.

1. False
2. True

Q. The energy radiated by a black body at $2300\text{K}$ is found to have maximum intensity at wavelength $1260\text{nm}$, its emissive power being $8000{\text{W/m}}^2$. When the body is cooled to a temperature $T\text{K}$, the emissive power is found to decrease to $500{\text{W/m}}^2$. Find the wavelength at which intensity of emission is maximum at the temperature $T$.

1. $1575\text{nm}$
2. $2520\text{nm}$
3. $1260\text{nm}$
4. $5040\text{nm}$

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. The power radiated by a black body is $P$ and it radiates maximum energy around wavelength ${\lambda }_{\circ }$. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength $3{\lambda }_{\circ }/4$, the power radiated by it will increase by a factor of

1. $\frac{4}{3}$
2. 
   $\frac{16}{9}$
3. 
   $\frac{64}{27}$
4. $\frac{256}{81}$

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

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

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. 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. If at temperature $T_1=1000K$, the wavelength is $1.4\times {10}^{-6}m$, then at what temperature the wavelength will be $2.8\times {10}^{-6}m$

1. 2000 K
2. 500 K
3. 250 K
4. None of these

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

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. Two spherical bodies A (radius $6\text{cm})$ and B (radius $18\text{cm})$ are at temperatures $T_1$ and $T_2$ , respectively. The maximum intensity in the emission spectrum of A is at $500\text{nm}$ and in that of B is at $1500\text{nm}$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?

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. $19200\AA$