Answer
Verified
411k+ views
Hint:We can use the Wien displacement law to find the wavelength at maximum energy ${\lambda _m}T = cons\tan t$. Where ${\lambda _m}$is the wavelength of maximum energy and T be the temperature. Blackbody is the surface that absorbs all the radiation falling on it that’s why it has the maximum energy.
Complete step by step answer:
Applying Wien displacement law: $\lambda T = $constant
$\lambda $ is the wavelength of maximum energy
$T$ is the absolute temperature
Using the given values from the question for black body
${\lambda _{m1}}{T_1} = {\lambda _{m2}}T{}_2$
Where we had taken ${\lambda _{m1 = }}14\mu m$, ${T_1} = 200K$, ${T_2} = 1000K$. ${\lambda _{m2}} = $?
Substituting the values
$14 \times 200 = {\lambda _{m2}} \times 1000$
$\Rightarrow{\lambda _{m2}} = \dfrac{{14 \times 200}}{{1000}}$
$\therefore{\lambda _{m2}} = 2.8\mu m$
Hence, the correct answer is C.
Additional information:
Wein displacement was named after the scientist Wilhelm Wien in the year $1893$ which states that black body radiation curve for different wavelengths will peak at different wavelengths that are inversely proportional to temperature. ${\lambda _m} = \dfrac{b}{T}$
Where ${\lambda _m}$ is the wavelength at maximum energy, $T$ is the absolute temperature and $b$ is the constant of proportionality called Wien’s displacement constant having value $2.89771 \ldots \times {10^{ - 3}}mK$
Note:Absolute temperature is the temperature of an object taken on a scale where $0$ is taken as absolute zero. Absolute zero is $0K$ or $ - 273.15^\circ C$ .All objects having absolute zero temperature emit electromagnetic radiation.
Complete step by step answer:
Applying Wien displacement law: $\lambda T = $constant
$\lambda $ is the wavelength of maximum energy
$T$ is the absolute temperature
Using the given values from the question for black body
${\lambda _{m1}}{T_1} = {\lambda _{m2}}T{}_2$
Where we had taken ${\lambda _{m1 = }}14\mu m$, ${T_1} = 200K$, ${T_2} = 1000K$. ${\lambda _{m2}} = $?
Substituting the values
$14 \times 200 = {\lambda _{m2}} \times 1000$
$\Rightarrow{\lambda _{m2}} = \dfrac{{14 \times 200}}{{1000}}$
$\therefore{\lambda _{m2}} = 2.8\mu m$
Hence, the correct answer is C.
Additional information:
Wein displacement was named after the scientist Wilhelm Wien in the year $1893$ which states that black body radiation curve for different wavelengths will peak at different wavelengths that are inversely proportional to temperature. ${\lambda _m} = \dfrac{b}{T}$
Where ${\lambda _m}$ is the wavelength at maximum energy, $T$ is the absolute temperature and $b$ is the constant of proportionality called Wien’s displacement constant having value $2.89771 \ldots \times {10^{ - 3}}mK$
Note:Absolute temperature is the temperature of an object taken on a scale where $0$ is taken as absolute zero. Absolute zero is $0K$ or $ - 273.15^\circ C$ .All objects having absolute zero temperature emit electromagnetic radiation.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE