To calculate the energy corresponding to light of wavelength $45$ nm, we use the formula for energy of a photon:$\\ E = \frac{hc}{\lambda} \\$Where:$\\$• $h = 6.63 \times 10^{-34}$ Js (Planck's constant)$\\$• $c = 3 \times 10^8$ m/s (speed of light)$\\$• $\lambda = 45$ nm$= 45 \times 10^{-9}$ m (wavelength)$\\$Substitute the known values into the formula:$\\ E = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{45 \times 10^{-9}} \\$Calculate the numerator:$\\ 6.63 \times 10^{-34} \times 3 \times 10^8 = 1.989 \times 10^{-25} \\$Calculate the denominator:$\\ 45 \times 10^{-9} = 4.5 \times 10^{-8} \\$Now, divide the numerator by the denominator:$\\ E = \frac{1.989 \times 10^{-25}}{4.5 \times 10^{-8}} \\$Perform the division:$\\ E = 4.42 \times 10^{-18}$ J$\\$Therefore, the energy corresponding to light of wavelength $45$ nm is $4.42 \times 10^{-18}$ J.$\\$This corresponds to Option 4.