Red light has a wavelength of 6.8E+2 nm. What is its frequency in 1/s, or Hz?

The frequency is 4.4 × 10¹⁴ s⁻¹.
The wavelength λ is the distance between successive peaks in a wave.

The frequency ##f## of a wave is the number of complete waves that pass a point in a given time.

The formula relating the frequency ##f## and wavelength λ is
##fλ = c or f = c/λ##
where ##c## is the speed of light.
In your case, ##λ## = 680 nm = 680 × 10⁻⁹ m and ##c## = 3.00 × 10⁸ m•s⁻¹.
∴ ##f = c/λ = (3.00 × 10⁸ m•s⁻¹)/(680 × 10⁻⁹ m)## = 4.4 × 10¹⁴ s⁻¹

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