Answer
a) Star B is blue.
b)$\dfrac{f_{A}}{f_{B}}$ = 0.36
Work Step by Step
a
The Wien's law says that
frequency is related to temperature as
$f_{peak}$ = 5.88 X $10^{10}$ X T.
For A,
$T_{A}$ = 4700 K
$f_{peak}$ = 5.88 X $10^{10}$ X T
$f_{peakA}$ = 5.88 X $10^{10}$ X 4700 = 2.76X $10^{14}$ Hz.
For B,
$T_{B}$ = 13000 K
$f_{peak}$ = 5.88 X $10^{10}$ X T
$f_{peakB}$ = 5.88 X $10^{10}$ X 13000 = 7.64 X $10^{14}$ Hz.
The frequency of blue[includes violet too] colour lies between 6.06–7.89 $10^{14}$ Hz.
Therefore, the blue star is B as it emits light with a higher frequency, which corresponds to blue in the colour spectrum.
b
f $\propto$ T
$\dfrac{f_{A}}{f_{B}}$ = $\dfrac{T_{A}}{T_{B}}$
$\dfrac{f_{A}}{f_{B}}$ = $\dfrac{4700}{13000}$ = 0.36.
