Final answer:
The corresponding range of frequencies for visible light, given wavelengths between 390 nm and 700 nm, is approximately 4.29 × 10¸ Hz to 7.69 × 10¸ Hz.
Step-by-step explanation:
To find the corresponding range of frequencies for visible light, we use the relationship between wavelength (λ), frequency (f), and the speed of light (c): c = λf. The speed of light is approximately 3.00 × 10¸ meters per second (m/s). Given the range of visible light wavelengths is between 3.9 × 10⁻⁷ m (390 nm) and 7.0 × 10⁻⁷ m (700 nm), we can calculate the frequencies using this formula.
The frequency for the shortest wavelength (390 nm) is calculated by dividing the speed of light by the wavelength:
f = c / λ = (3.00 × 10¸ m/s) / (3.9 × 10⁻⁷ m) = 7.69 × 10¸ Hz
Similarly, the frequency for the longest wavelength (700 nm) is:
f = c / λ = (3.00 × 10¸ m/s) / (7.0 × 10⁻⁷ m) = 4.29 × 10¸ Hz
Therefore, the range of frequencies for visible light is from 4.29 × 10¸ Hz to 7.69 × 10¸ Hz. Note: The actual range will be slightly different because the exact values have been rounded for the speed of light and the wavelengths.