The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the temperature (in K) of the black body is

To find the new temperature of the black body, we can apply Wien's Displacement Law.

Wien's Displacement Law states that the peak wavelength of radiation emitted by a black body is inversely proportional to its absolute temperature:
${\lambda }_{\text{max}}·T=\text{constant}$
This can also be written as:
${\lambda }_1{T}_1={\lambda }_2{T}_2$

From the given problem, we have the following values:
Initial peak wavelength, ${\lambda }_1=1.45 \mu \text{m}$
Initial temperature, $T_1=2000 \text{K}$
New peak wavelength, ${\lambda }_2=2.90 \mu \text{m}$

Let $T_2$ be the new temperature of the black body. Rearranging the formula to solve for $T_2$:
$T_2=\frac{{\lambda }_1{T}_1}{{\lambda }_2}$

Substituting the values into the equation:
$T_2=\frac{1.45·2000}{2.90}$

Since 2.90 is exactly twice 1.45, we can simplify this expression:
$T_2=\frac{2000}{2}=1000 \text{K}$

Thus, the new temperature of the black body is 1000 K.