Answer
(a) $\lambda = 400~nm$
(b) $f = 7.5\times 10^{14}~Hz$
Work Step by Step
(a) We can convert the energy to units of joules:
$E = 3.1~eV\times \frac{1.6\times 10^{-19}~J}{1~eV} = 4.96\times 10^{-19}~J$
We can find the wavelength:
$E = \frac{hc}{\lambda}$
$\lambda = \frac{hc}{E}$
$\lambda = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{4.96\times 10^{-19}~J}$
$\lambda = 4.0\times 10^{-7}~m$
$\lambda = 400~nm$
(b) We can find the frequency:
$\lambda~f = c$
$f = \frac{c}{\lambda}$
$f = \frac{3.0\times 10^8~m/s}{4.0\times 10^{-7}~m}$
$f = 7.5\times 10^{14}~Hz$
