The Apparent Brightness of a Star Is $1.0 \times 10 ^ { - 12 } \mathrm {~W} / \mathrm { m } ^ { 2 }$

Multiple Choice

The apparent brightness of a star is $1.0 \times 10 ^ { - 12 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ and the peak wavelength in its light is 600 $\mathrm { nm }$ . Assuming it is the same size as our sun and that it radiates like an ideal blackbody, estimate its distance from us, in parsecs. The constant in Wien's law is $0.00290 \mathrm {~m} \cdot \mathrm { K }$ , and 1 parsec is equal to $3.09 \times 10 ^ { 16 } \mathrm {~m} . \left( R _ { \text {sun } } = 6.96 \times 108 \mathrm {~m} , \sigma = 5.67 \times 10 ^ { - 8 } \frac { \mathrm { W } } { \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } } \right)$

A) $1.2 \mathrm { pc }$
B) $120 \mathrm { pc }$
C) $1200 \mathrm { pc }$
D) $12 \mathrm { pc }$