Question

Violet light has a frequency of 7.26 × 1014 Hz and travels at a speed of 3.00 × 108 m/s.

The wavelength of violet light, rounded to the nearest nanometer, is

Answer 1

To find the wavelength of violet light, we can use the wave equation:

\[
\text{wavelength} (\lambda) = \frac{\text{speed} (v)}{\text{frequency} (f)}
\]

Given:
- Speed of light, \( v = 3.00 \times 10^8 \text{ m/s} \)
- Frequency of violet light, \( f = 7.26 \times 10^{14} \text{ Hz} \)

Substituting the values into the equation:

\[
\lambda = \frac{3.00 \times 10^8 \text{ m/s}}{7.26 \times 10^{14} \text{ Hz}}
\]

Calculating the wavelength:

\[
\lambda \approx \frac{3.00}{7.26} \times 10^{8 - 14} \text{ m} = \frac{3.00}{7.26} \times 10^{-6} \text{ m}
\]

Calculating \( \frac{3.00}{7.26} \):

\[
\frac{3.00}{7.26} \approx 0.412
\]

Now, substituting back:

\[
\lambda \approx 0.412 \times 10^{-6} \text{ m} = 4.12 \times 10^{-7} \text{ m}
\]

To convert meters to nanometers, we can use the conversion \( 1 \text{ m} = 1 \times 10^{9} \text{ nm} \):

\[
\lambda \approx 4.12 \times 10^{-7} \text{ m} \times 10^{9} \text{ nm/m} \approx 412 \text{ nm}
\]

Rounding to the nearest nanometer, the wavelength of violet light is:

\[
\lambda \approx 412 \text{ nm}
\]

Thus, the final answer is:

**412 nm**