What is the wavelength of blue light that has a frequency of 6.17 × 10¹⁴ s⁻¹? (c = 3.00 × 10⁸ m/s)

To find the wavelength (\(\lambda\)) of blue light, we can use the formula that relates the speed of light (\(c\)), the frequency (\(f\)), and the wavelength (\(\lambda\)):

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

Where:
- \(c = 3.00 \times 10^8 \, \text{m/s}\) is the speed of light,
- \(f = 6.17 \times 10^{14} \, \text{s}^{-1}\) is the frequency.

Now, let's calculate the wavelength:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{6.17 \times 10^{14} \, \text{s}^{-1}}
\]

Let me solve this for you.The wavelength (\(\lambda\)) of blue light with a frequency of \(6.17 \times 10^{14} \, \text{s}^{-1}\) is approximately \(4.86 \times 10^{-7} \, \text{m}\), or 486 nanometers (nm).

Would you like more details on how this calculation works, or do you have any questions?

Here are some related questions to expand your understanding:
1. How does wavelength change with frequency in the electromagnetic spectrum?
2. What is the typical wavelength range for different colors of visible light?
3. How do you calculate the energy of a photon given its frequency?
4. What are the practical applications of blue light in technology and science?
5. How does the wavelength of light affect its ability to pass through different materials?

**Tip**: Remember, the shorter the wavelength of light, the higher the frequency and energy!

Discover how to calculate the wavelength of blue light with a frequency of 6.17 × 10¹⁴ s⁻¹ using the wave equation. This problem involves core concepts from physics, including the speed of light and the relationship between frequency and wavelength. Suitable for high school students in Grades 10-12.

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