Answer:
Approximately [tex]1.73 \times 10^{-15}\; {\rm s^{-1}}[/tex] (or equivalently, [tex]1.73 \times 10^{-15}\; {\rm Hz}[/tex]) assuming that the wavelength was measured in vacuum.
Explanation:
Look up the speed of light in vacuum: [tex]v \approx 3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}[/tex].
Wavelength [tex]\lambda[/tex] is the distance the wave travelled in one period [tex]T[/tex] of time. Hence, multiplying period by the speed [tex]v[/tex] of the wave will give the wavelength of the wave: [tex]\lambda = v\, T[/tex]. Rearrange to obtain [tex]T = (\lambda / v)[/tex].
The frequency [tex]f[/tex] of a wave is the number of periods of this wave in unit time. Frequency is equal to the reciprocal of period: [tex]f = (1/T)[/tex]. However, since [tex]T = (\lambda / v)[/tex]:
[tex]\begin{aligned}f &= \frac{1}{T} \\ &= \frac{1}{\lambda / v} \\ &= \frac{v}{\lambda}\end{aligned}[/tex].
Apply unit conversion and ensure that the wavelength of this wave is measured in standard units:
[tex]\begin{aligned}\lambda &= (519\; {\rm nm})\, \frac{10^{-9}\; {\rm m}}{1\; {\rm nm}} \\ &= 5.19 \times 10^{-7}\; {\rm m}\end{aligned}[/tex].
The speed of the wave in this question is equal to the speed of light in vacuum, [tex]v \approx 3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}[/tex]. Substitute in the value of wave speed [tex]v[/tex] and wavelength [tex]\lambda[/tex] to find the frequency [tex]f[/tex] of this wave:
[tex]\begin{aligned}f &= \frac{v}{\lambda} \\ &\approx \frac{3.00\times 10^{8}\; {\rm m\cdot s^{-1}}}{5.19 \times 10^{-7}\; {\rm m}} \\ &\approx 1.73 \times 10^{-15}\; {\rm s^{-1}} \\ &= 1.73\times 10^{-15}\; {\rm Hz}\end{aligned}[/tex].
