Answer
The 4.257 $μm$ radiation requires greater energy.
4.257 $μm$ needs $4.666 \times 10^{-20} J$
15.00 $μm$ needs $1.324 \times 10^{-20} J$
Work Step by Step
According to Plank's theory, the wavelength is inversely proportional to the energy; therefore, the radiation with smaller wavelength is the one that requires less energy.
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μ = $10^{-6}$;
$4.257 μm = 4.257 \times 10^{-6}m$
$Energy = \frac{hc}{λ} = \frac{6.626 \times 10^{-34} \times 2.998 \times 10^8}{4.257 \times 10^{-6}} = 4.666 \times 10^{-20} J$
$15.00 μm = 15.00 \times 10^{-6}m$
$Energy = \frac{hc}{λ} = \frac{6.626 \times 10^{-34} \times 2.998 \times 10^8}{15.00 \times 10^{-6}} = 1.324 \times 10^{-20} J$
