The peak in the radiation spectrum of a star X is at a wavelength of 300 nm.

Show that the surface temperature of star X is about 10000 K. 

The radius of star X is 4.5 R_S where R_S is the radius of the Sun. The surface temperature of the Sun is 5.7×10³ K.

On the Hertzsprung–Russell diagram, label the position of star X with the letter X.

$T = \frac{{2.9 \times {{10}^{ - 3}}}}{{3.0 \times {{10}^{ - 7}}}}$;
9700 (K);

$\frac{{{L_X}}}{{{L_S}}} = \frac{{\sigma {r_x}^2{T_x}^4}}{{\sigma {r_S}^2{T_S}^4}}$;
=$\frac{{{{4.5}^2} \times {{9700}^4}}}{{{{5700}^4}}}$;
=170;

Accept answers that use T = 10000(K) to give an answer of 190.

X marked correctly within range shown;