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The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the centre of a star of radius r, whose outer surface radiates as a black body at a temperature T K is given by

(where \sigma is Stefan's constant)

  • Option 1)

    \frac{4\sigma\pi\text{r}^{2}\text{T}^{4}}{\text{R}^{2}}

  • Option 2)

    \frac{\sigma\text{r}^{2}\text{T}^{4}}{\text{R}^{2}}

  • Option 3)

    \frac{\sigma\text{r}^{2}\text{T}^{4}}{4\pi\text{R}^{2}}

  • Option 4)

    \frac{\sigma\text{r}^{4}\text{T}^{4}}{\text{R}^{4}}

    (Where \sigma is Stefan's constant)

 

Answers (1)

best_answer

As we have leaqrned @2747 

 Power of radiation P = \sigma AT^4

P = \sigma (4 \pi r^2)T^4.....(1)

Intensity of this energy at a distance R is 

I = \frac{P }{4 \pi R^2}= \frac{\sigma (4r^2)T^4}{R^2}

I = \frac{\sigma r^2T^4 }{ R^2}


Option 1)

\frac{4\sigma\pi\text{r}^{2}\text{T}^{4}}{\text{R}^{2}}

Option 2)

\frac{\sigma\text{r}^{2}\text{T}^{4}}{\text{R}^{2}}

Option 3)

\frac{\sigma\text{r}^{2}\text{T}^{4}}{4\pi\text{R}^{2}}

Option 4)

\frac{\sigma\text{r}^{4}\text{T}^{4}}{\text{R}^{4}}

(Where \sigma is Stefan's constant)

Posted by

SudhirSol

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