Answer:
[tex]2.89\times 10^{-12}\ m[/tex]
[tex]\lambda_m=2.75238\times 10^{-9}\lambda_{mc}[/tex]
Explanation:
b = Wien's displacement constant = [tex]2.89\times 10^{-3}\ mK[/tex]
T = Temperature = [tex]10^9\ K[/tex]
[tex]\lambda_m[/tex] = Peak wavelength
From Wien's displacement law we have
[tex]\lambda_m=\frac{b}{T}\\\Rightarrow \lambda_m=\frac{2.89\times 10^{-3}}{10^9}\\\Rightarrow \lambda_m=2.89\times 10^{-12}\ m[/tex]
The peak wavelength would be [tex]2.89\times 10^{-12}\ m[/tex]
Current peak wavelength is
[tex]\lambda_{mc}=\frac{b}{T}\\\Rightarrow \lambda_m=\frac{2.89\times 10^{-3}}{2.73}\\\Rightarrow \lambda_m=0.00105\ m[/tex]
Comparing
[tex]\frac{\lambda_m}{\lambda_{mc}}=\frac{2.89\times 10^{-12}}{0.00105}\\\Rightarrow \lambda_m=2.75238\times 10^{-9}\lambda_{mc}[/tex]
[tex]\lambda_m=2.75238\times 10^{-9}\lambda_{mc}[/tex]
