Answer
a) 1.6 $\times 10^{11}$ Hz
b) 1.87 $\times 19^{-3}$ m
Work Step by Step
a
The temperature of the blackbody is 2.7 K.
The frequency can be found using Wien's Displacement Law:
$f_{peak}$ = 5.88 X $10^{10}$ X T
$f_{peak}$ = 5.88 X $10^{10}$ X 2.7 = 1.6 X $10^{11}$ Hz.
b
The wavelength and frequency are related as
$\lambda $ f = c. So
$\lambda$ X 1.6 X $10^{11}$ = 3 X $10^{8}$
$\lambda$ = $\dfrac{3}{1.6}$ X $10^{-3}$ m = $1.87$ X $10^{-3}$ m.
