Answer :
Frequency and energy of least energetic photons is [tex]1.24*10^{15}[/tex] Hz and [tex]8.2*10^{-19}[/tex] J respectively.
As frequency is inversely proportional to wavelength, the least energetic photon will have highest wavelength. So, the given wavelength is highest, which is ≤ 242 nm.
Now, we know, 1 nm = [tex]10^{-9}[/tex] m
λ [tex]= 2.42*10^{-7}[/tex] m
Now, using the relation -
c = fλ, where c is speed of light, f is frequency and λ is wavelength
Also, c = [tex]3*10^{8}[/tex] m/s
f = c/λ
f = [tex]\frac{3*10^{8}} {2.42*10^{-7}}[/tex]
f = [tex]1.24*10^{15}[/tex] Hz
Now, calculating energy by the formula -
E = hf, where E is energy, h is planck's constant and f is frequency.
As, we know, h = [tex]6.63*10^{-34}[/tex] Js
E = [tex]6.63*10^{-34}[/tex]* [tex]6.63*10^{-34}[/tex]
E = [tex]8.2*10^{-19}[/tex] J
Hence, the frequency and energy of the least energetic of these photons is [tex]1.24*10^{15}[/tex] Hz and [tex]8.2*10^{-19}[/tex] J respectively.
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