Final answer:
The frequency of light with a given wavelength can be calculated using the wave equation, c = λf. The wavelength of light with a given frequency can be calculated using the same equation, rearranged. For a wavelength of 1.87 x 10⁻¹⁴ m, the frequency is 1.60 x 10¹⁴ Hz. For a frequency of 5.6 x 10⁻¹⁴ Hz, the wavelength is 5.36 x 10⁻⁶ m.
Step-by-step explanation:
To find the frequency of light with a given wavelength, we can use the wave equation, c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. Rearranging the equation, we have f = c/λ. For the first question, with a wavelength of 1.87 x 10⁻¹⁴ m, the frequency can be calculated as follows:
f = c/λ = (3.00 x 10⁸ m/s) / (1.87 x 10⁻¹⁴ m) = 1.60 x 10¹⁴ Hz
Therefore, the frequency of light with a wavelength of 1.87 x 10⁻¹⁴ m is 1.60 x 10¹⁴ Hz.
For the second question, with a frequency of 5.6 x 10⁻¹⁴ Hz, the wavelength can be calculated as follows:
λ = c/f = (3.00 x 10⁸ m/s) / (5.6 x 10⁻¹⁴ Hz) = 5.36 x 10⁻⁶ m
Therefore, the wavelength of light with a frequency of 5.6 x 10⁻¹⁴ Hz is 5.36 x 10⁻⁶ m.