Question

According to Wien's Law, how many times hotter is an object whose blackbody emission spectrum peaks in the blue, at a wave length of 450 nm, than a object whose spectrum peaks in the red, at 700 nm? Please show me your calculations.

Answer 1

Answer:1.55 times

Explanation:

Given

First wavelength$(\lambda _1)=450 nm$

Second wavelength$(\lambda _2)=700 nm$

According wien's diplacement law

$\lambda T=constant$

where $\lambda =wavelength$

T=Temperature

Let $T_1 and T_2$ be the temperatures corresponding to $\lambda _1 & \lambda _2$ respectively.

$\lambda _1\times T_1=\lambda _2\times T_2$

$\frac{T_1}{T_2}=\frac{\lambda _2}{\lambda _1}$

$\frac{T_1}{T_2}=\frac{700}{450}=1.55$

Thus object with $\lambda 450 nm$ is 1.55 times hotter than object with wavelength $\lambda =700 nm$