According to Wein's displacement law,

${\lambda _m}T$ = 2.88 × 10^–3

When T = 2000 K,

${\lambda _m}$(2000) = 2.88 × 10^–3   ....(1)

When T = 3000 K,

$\lambda _m^{'}$ (3000) = 2.88 × 10^–3    ....(2)

Dividing (1) by (2),

${2 \over 3}{{{\lambda _m}} \over {\lambda _m^{'}}} = 1$

$\Rightarrow {{{\lambda _m}} \over {\lambda _m^{'}}} = {3 \over 2}$

$\Rightarrow \lambda _m^{'} = {2 \over 3}{\lambda _m}$