Answer
$\lambda_{max} = 2.9\times 10^{-10}~m$
Work Step by Step
We can find the wavelength at which the thermal radiation is maximum:
$\lambda_{max}~T = 2.898\times 10^{-3}~m~K$
$\lambda_{max} = \frac{2.898\times 10^{-3}~m~K}{T}$
$\lambda_{max} = \frac{2.898\times 10^{-3}~m~K}{1.0\times 10^7~K}$
$\lambda_{max} = 2.9\times 10^{-10}~m$
