Question

Yellow light has a frequency of 5.2 × 1014 Hz and travels at a speed of 3.0 × 108 m/s. What is the wavelength of yellow light, in meters?

5.8 × 10–7 m
2.2 × 10–6 m
1.7 × 106 m
8.2 × 1022 m

Answer 1

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

\[
c = f \times \lambda
\]

Rearranging this formula to solve for the wavelength gives us:

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

Given:
- Speed of light, \(c = 3.0 \times 10^8 \text{ m/s}\)
- Frequency, \(f = 5.2 \times 10^{14} \text{ Hz}\)

Now, we can substitute the values into the equation:

\[
\lambda = \frac{3.0 \times 10^8 \text{ m/s}}{5.2 \times 10^{14} \text{ Hz}}
\]

Calculating this gives us:

\[
\lambda = \frac{3.0}{5.2} \times \frac{10^8}{10^{14}} \text{ m}
\]

Calculating the numerical part:

\[
\frac{3.0}{5.2} \approx 0.5769
\]

Now for the powers of ten:

\[
\frac{10^8}{10^{14}} = 10^{-6}
\]

Now putting it all together:

\[
\lambda \approx 0.5769 \times 10^{-6} \text{ m}
\]

Converting this to scientific notation:

\[
\lambda \approx 5.769 \times 10^{-7} \text{ m}
\]

Rounding this to two significant figures gives:

\[
\lambda \approx 5.8 \times 10^{-7} \text{ m}
\]

Thus, the wavelength of yellow light is \( \mathbf{5.8 \times 10^{-7} \text{ m}} \).