Answer
Quantum of violet light has more energy than quantum of red light.
$\frac{E_{violet,quanta}}{E_{red,quanta}}=1.75=\frac{7}{4}$
Work Step by Step
Energy of a Quanta of light is given by $E=hf$, since $f=\frac{c}{\lambda}$
Energy of a Quanta of light is $E=\frac{hc}{\lambda}$
wavelength of red light $\lambda_{red}= 700nm=700\times10^{-9}m=7\times10^{-7}m$
$h=6.63\times10^{-34} J.s$, $c=3\times10^{8}m/s$
putting these values we will get
$E_{red,quanta}=\frac{6.63\times10^{-34} J.s\times3\times10^{8}m/s}{7\times10^{-7}m}$
$E_{red,quanta}=2.8414\times10^{-19}J$
similarly for violet light
wavelength of violet light $\lambda_{red}= 400nm=400\times10^{-9}m=4\times10^{-7}m$
$h=6.63\times10^{-34} J.s$, $c=3\times10^{8}m/s$
putting these values we will get
$E_{violet,quanta}=\frac{6.63\times10^{-34} J.s\times3\times10^{8}m/s}{4\times10^{-7}m}$
$E_{violet,quanta}=4.9725\times10^{-19}J$
ratio of the photon energy associated with voilet light to that related to red light
$\frac{E_{violet,quanta}}{E_{red,quanta}}=\frac{4.9725\times10^{-19}J}{2.8414\times10^{-19}J}= 1.75=\frac{175}{100}=\frac{7}{4}$
