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

Question

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