A black body has maximum wavelength ${\mathrm{\lambda }}_{\mathrm{m}}$ at 2000 K. Its corresponding wavelength at 3000 K will be

• A

  $\frac{16}{81}{\mathrm{\lambda }}_{\mathrm{m}}$

• B

  $\frac{81}{16}{\mathrm{\lambda }}_{\mathrm{m}}$

• C

  $\frac{3}{2}{\mathrm{\lambda }}_{\mathrm{m}}$

• D

  $\frac{2}{3}{\mathrm{\lambda }}_{\mathrm{m}}$