Question

The wavelength of maximum intensity of radiation emitted by a star is 289.8 nm. The radiation intensity for the star is : (Stefan’s constant $5.67\times {10}^{-8}W{m}^{-2}{K}^{-4}$, constant $b=2898\mu mK)$

• A. $5.67\times {10}^{8}W/m^2$
  
  
• B. $5.67\times {10}^{12}W/m^2$
  
  
• C. $10.67\times {10}^{7}W/m^2$
  
  
• D. $10.67\times {10}^{14}W/m^2$

Answer 1

The correct option is A $5.67\times {10}^{8}W/m^2$



We know ${\lambda }_{max}T=b$
$\Rightarrow T=\frac{b}{{\lambda }_{max}}=\frac{2898\times {10}^{-6}}{289.8\times {10}^{-9}}={10}^{4}K$
According to Stefan's Law
$E=\sigma T^4=(5.67\times {10}^{-8})({10}^4{)}^4=5.67\times {10}^{8}W/m^2$