Answer
Given,
Sirius A surface temperature,T = 9400 K
Sirius A luminosity,L = 26 L₀
L₀ is the luminosity of sun.
Radius of sun = 695700000 m
Temperature on sun surface = 5780 K
Luminous intensity is given by:-
[tex]L=4 \pi R^{2} \sigma T^{4}[/tex]
Now
[tex]\frac{L}{L_{0}}=\frac{4 \pi R^{2} \sigma T^{4}}{4 \pi R_{0}^{2} \sigma T_{0}^{4}}=26[/tex]
[tex]\Rightarrow \frac{R^{2} T^{4}}{R_{0}^{2} T_{0}^{4}}=26[/tex]
[tex]\Rightarrow R^{2}=26 \times \frac{R^{2} T_{0}^{4}}{T^{4}}=26 \times \frac{695700000^{2} \times 5780^{4}}{9400^{4}}[/tex]
[tex]R=1341246640\ m=1.34 \times 10^{9}[/tex]
The radius of Sirius will be "1.34 × 10⁹".
According to the question,
Temperature of surface, T = 9400 K
Sun's radius, R = 695700000 m
Sun's surface temperature = 5780 K
Luminosity of Sirius A, L = 26 L₀
Here, L₀ = Sun's luminosity
We know the formula,
→ Luminous intensity,
L = 4πR²σT⁴
then,
→ [tex]\frac{L}{L_0} = \frac{4 \pi R^2 \sigma T^4}{4 \pi R_0^2 \sigma T_0^4}[/tex] = 26
or,
[tex]\frac{R^2T^4}{R_0^2 T_0^4}[/tex] = 26
hence,
The radius will be:
→ R² = 26 × [tex]\frac{R^2 T_0^4}{T^4}[/tex]
By substituting the values, we get
= 26 × [tex]\frac{(695700000)^2 (5780)^4}{(9400)^4}[/tex]
= 1341246640 m
= 1.34 × 10⁹
Thus the above answer i correct.
Find out more information about Luminous intensity here:
https://brainly.com/question/11719996
