Question

The wavelengths of visible light vary from about 3 x 10-7 m to 7 x 10-7 m. What is the range of
frequencies of visible light in a vacuum? (1 point)

90 Hz to 210 Hz

9 - 1010 Hz to 2.1 . 1011 Hz

4.28 - 105 Hz to 1 . 106 Hz

4.29 - 1014 Hz to 1 . 1015 Hz

Answer 1

To find the range of frequencies of visible light, you can use the formula:

\[
f = \frac{c}{\lambda}
\]

where:
- \( f \) is the frequency,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength.

We're given the range of wavelengths for visible light:
- Minimum wavelength, \( \lambda_{\text{min}} = 3 \times 10^{-7} \) m
- Maximum wavelength, \( \lambda_{\text{max}} = 7 \times 10^{-7} \) m

Now, let's calculate the frequencies for these wavelengths.

1. For the minimum wavelength (\( 3 \times 10^{-7} \) m):

\[
f_{\text{min}} = \frac{c}{\lambda_{\text{max}}} = \frac{3 \times 10^8 \, \text{m/s}}{7 \times 10^{-7} \, \text{m}} \approx \frac{3 \times 10^8}{7 \times 10^{-7}} \approx 4.29 \times 10^{14} \, \text{Hz}
\]

2. For the maximum wavelength (\( 7 \times 10^{-7} \) m):

\[
f_{\text{max}} = \frac{c}{\lambda_{\text{min}}} = \frac{3 \times 10^8 \, \text{m/s}}{3 \times 10^{-7} \, \text{m}} \approx \frac{3 \times 10^8}{3 \times 10^{-7}} \approx 1.0 \times 10^{15} \, \text{Hz}
\]

Thus, the range of frequencies for visible light in a vacuum is approximately:

\[
4.29 \times 10^{14} \, \text{Hz} \text{ to } 1.0 \times 10^{15} \, \text{Hz}
\]

The correct answer is:

**4.29 - 10^14 Hz to 1 - 10^15 Hz**.