
On observing light from three different stars $P,\;Q,\;R$, it was found that intensity of violet colour is maximum in the spectrum of $P$, the intensity of green colour is maximum in the spectrum of $R$ and the intensity of red colour is maximum in the spectrum of $Q$. If $T_{P},T_{Q}$ and $T_{R}$ are the respective absolute temperature of $P,\;Q$ and $R$, then it can be concluded from the above observation that:
\[\begin{align}
& A.{{T}_{P}}<{{T}_{R}}<{{T}_{Q}} \\
& B.{{T}_{P}}<{{T}_{Q}}<{{T}_{R}} \\
& C.{{T}_{P}}>{{T}_{Q}}>{{T}_{R}} \\
& D.{{T}_{P}}>{{T}_{R}}>{{T}_{Q}} \\
\end{align}\]
Answer
544.5k+ views
Hint: We know that the rate at which a body absorbs heat is given by the Stefan–Boltzmann law. However, Wien’s law of displacement, that the radiation due to a body varies with temperature. Since we need the temperature due to maximum wavelength, we are using the Wien’s law here.
Formula used:
$T=\dfrac{1}{\lambda_{m}}$
Complete step-by-step answer:
Wien’s law of displacement, gives the temperature of the maximum wavelength from the black-body radiation curve. Then, we have, $\lambda_{m}T=b$. where, $\lambda_{m}$ is the maximum wavelength, whose corresponding temperature is $T$ and $b$ is some consonant.
Clearly, we have, $T=\dfrac{1}{\lambda_{m}}$
We know that the red has the highest wavelength, then star Q will have the minimum wavelength. Followed by green, then the star R will have the second largest value of temperature. And violet has the lowest wavelength or P has the highest temperature.
Hence the correct option is \[D.{{T}_{P}}>{{T}_{R}}>{{T}_{Q}}\]
So, the correct answer is “Option D”.
Additional Information: Stefan-Boltzmann constant or the Stefan’s constant is denoted by $\sigma$, it is a constant of proportionality, used in the Stefan–Boltzmann law of blackbody radiation; which is stated as the total intensity radiated over the wavelength, it is proportional the temperature. It is given as $E_{ab}=\sigma AT^{4}$ where $E_{ab}$ is the energy absorbed by the body here the star, whose surface area is $A$ and temperature is $T$.
Note: A German physicist Max Planck in the 1900, gave the theory of black body radiations, he stated that the spectral lines of a hypothetical black body would emit radiations in small, discrete packets called the quanta of energy, and not as continuous radiation as expected. Here, we are assuming the stars to be a black body.
Formula used:
$T=\dfrac{1}{\lambda_{m}}$
Complete step-by-step answer:
Wien’s law of displacement, gives the temperature of the maximum wavelength from the black-body radiation curve. Then, we have, $\lambda_{m}T=b$. where, $\lambda_{m}$ is the maximum wavelength, whose corresponding temperature is $T$ and $b$ is some consonant.
Clearly, we have, $T=\dfrac{1}{\lambda_{m}}$
We know that the red has the highest wavelength, then star Q will have the minimum wavelength. Followed by green, then the star R will have the second largest value of temperature. And violet has the lowest wavelength or P has the highest temperature.
Hence the correct option is \[D.{{T}_{P}}>{{T}_{R}}>{{T}_{Q}}\]
So, the correct answer is “Option D”.
Additional Information: Stefan-Boltzmann constant or the Stefan’s constant is denoted by $\sigma$, it is a constant of proportionality, used in the Stefan–Boltzmann law of blackbody radiation; which is stated as the total intensity radiated over the wavelength, it is proportional the temperature. It is given as $E_{ab}=\sigma AT^{4}$ where $E_{ab}$ is the energy absorbed by the body here the star, whose surface area is $A$ and temperature is $T$.
Note: A German physicist Max Planck in the 1900, gave the theory of black body radiations, he stated that the spectral lines of a hypothetical black body would emit radiations in small, discrete packets called the quanta of energy, and not as continuous radiation as expected. Here, we are assuming the stars to be a black body.
Recently Updated Pages
Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

If overrightarrow a overrightarrow b overrightarrow class 12 maths CBSE

If a b and c are unit coplanar vectors then left 2a class 12 maths CBSE

Master Class 12 Economics: Engaging Questions & Answers for Success

Trending doubts
Draw ray diagrams each showing i myopic eye and ii class 12 physics CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?

One megawatt is equal to how many units of electri class 12 physics CBSE

How will you obtain OR AND gates from the NAND and class 12 physics CBSE

Differentiate between exergonic and endergonic rea class 12 biology CBSE

