Match the temperature of a black body given in List-$I$ with an appropriate statement in List-$II$, and choose the correct option.
[Given: Wien's constant as $2.9 \times 10^{-3} \mathrm{~m}-\mathrm{K}$ and $\frac{\mathrm{hc}}{\mathrm{e}}=1.24 \times 10^{-6} \mathrm{~V}-\mathrm{m}$ ]
| List-$I$ | List-$II$ |
| ($P$) $2000 \mathrm{~K}$ | ($1$) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function $4 \mathrm{eV}$ |
| ($Q$) $3000 \mathrm{~K}$ | ($2$) The radiation at peak wavelength is visible to human eye. |
| ($R$) $5000 \mathrm{~K}$ | ($3$) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction. |
| ($S$) $10000 \mathrm{~K}$ | ($4$) The power emitted per unit area is $1 / 16$ of that emitted by a blackbody at temperature $6000 \mathrm{~K}$. |
| ($5$) The radiation at peak emission wavelength can be used to image human bones. |
IIT 2023, Advanced
Download our app for free and get started
$\Rightarrow$ For option $(\mathrm{P})$ temperature is minimum hence $\lambda \mathrm{m}$ will be maximum $\beta=\frac{\lambda \mathrm{D}}{\mathrm{d}} \Rightarrow \beta$ will also be maximum
$\Rightarrow \text { For option (Q) } \mathrm{T}=3000$
$\lambda \mathrm{m}=\frac{\mathrm{b}}{\mathrm{T}}=\frac{2.9 \times 10^{-3}}{30000}$
$\lambda \mathrm{m}=\frac{2.9}{3} \times 10^{-6}$
$=0.96 \times 10^{-6}$
$=966.6 \mathrm{~nm}$
$\mathrm{P}_{3000}=6 \mathrm{~A}(3000)^{4}$
$\mathrm{P}_{6000}=6 \mathrm{~A}(6000)^{4}$
$\frac{\mathrm{P}_{3000}}{\mathrm{P}_{6000}}=\left(\frac{1}{2}\right)^4=\frac{1}{16}$
$\mathrm{P}_{3000}=\frac{1}{16} \mathrm{P}_{\text {क000 }}$
$\text { Q-4 }$
$\Rightarrow \text { For }(R) T=5000 \mathrm{~K}$
$\lambda \mathrm{m}=\frac{2.9 \times 10^{-3}}{5 \times 10^3}=0.58 \times 10^{-6}$
$=580 \mathrm{~mm}$
Visible to human eyes
$R-2$
$\Rightarrow$ For ($S$) $T=10,000 \rightarrow$ maximum
Hence $(3)$ is wrong as it has mmmmum ( $\lambda \mathrm{m})$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two thin metallic spherical shells of radii ${r}_{1}$ and ${r}_{2}$ $\left({r}_{1}<{r}_{2}\right)$ are placed with their centres coinciding. A material of thermal conductivity ${K}$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}\left(\theta_{1}<\theta_{2}\right)$. The rate at which heat flows radially through the material is :-View Solution
- 2Consider two rods of same length and different specific heats $\left(S_{1}, S_{2}\right)$, conductivities $\left(K_{1}, K_{2}\right)$ and area of cross-sections $\left(A_{1}, A_{2}\right)$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If rate of loss of heat due to conduction is equal, thenView Solution
- 3The temperature drop through each layer of a two layer furnace wall is shown in figure. Assume that the external temperature $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thickness of the layers $x_1$ and $x_2$ are the same, which of the following statements are correct.View Solution
- 4An object is cooled from $75°C$ to $65°C$ in $2$ minutes in a room at $30°C$ . The time taken to cool another object from $55°C$ to $45°C$ in the same room in minutes isView Solution
- 5View SolutionThe dimensional formula for thermal resistance is
- 6Two identical objects $A$ and $B$ are at temperatures $T_A$ and $T_B$ respectively. Both objects are placed in a room with perfectly absorbing walls maintained at temperatures T $({T_A} > T > {T_B}).$ The objects A and B attain temperature $T $ eventually which one of the following is correct statementView Solution
- 7The temperature of the body is increased from $-73^o C\, to \,327^o C$, the ratio of energy emitted per second is :View Solution
- 8A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at $0 K$. At time $t =0$, the temperature of the object is $200 K$. The temperature of the object becomes $100 K$ at $t = t _1$ and $50 K$ at $t = t _2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $\left( t _2 / t _1\right)$ is. . . . .View Solution
- 9A calorimeter of mass $0.2$ kg and specific heat $900 J/kg-K$ . Containing $0.5$ kg of a liquid of specific heat $2400J /kg-K$ . Its temperature falls from ${60^o}C\,{\rm{to}}\,\,{\rm{5}}{{\rm{5}}^{\rm{o}}}C$ in one minute. The rate of cooling is ....... $J/s$View Solution
- 10A black body is heated from ${27^o}C$ to ${127^o}C$. The ratio of their energies of radiations emitted will beView Solution