Answer:
Wien peak ( λmax ) is 107.40 nm
radius of super giant is 1.086 × m
Explanation:
given data
temperature 27 kK
power = 100000 times of Sun
Sun radius = 6.96 × 10^8 m
to find out
Wien peak ( λmax ) and radius of supergiant (r)
solution
we will apply here first wien law to find Wien peak that is
λmax = b / t
λmax = 2.9 × / 27000 = 1.0740 ×
so Wien peak ( λmax ) is 107.40 nm
and
now we apply steafay law that is
P = σ × A × .........................1
and we know total power output 100000 time of Sun
so we say
4πr²s = 100000 × 4πR²s
r² = 100000 × R² /
put here value
r² = 100000 × (6.96× )² ×
/
r² = 1.18132 ×
r = 1.086 × m
so radius of super giant is 1.086 × m