Question

Green light has a wavelength of about 510 nm and travels at a speed of 3.00 × 108 m/s.

The frequency of green light, rounded to the nearest tenth and written in scientific notation, is what?

Answer 1

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

\[
c = f \cdot \lambda
\]

Where:
- \(c\) is the speed of light (3.00 × 10^8 m/s),
- \(f\) is the frequency (in Hz),
- \(\lambda\) is the wavelength (in meters).

Given that the wavelength of green light is 510 nm, we first need to convert this wavelength into meters:

\[
510 \, \text{nm} = 510 \times 10^{-9} \, \text{m}
\]

Now we can rearrange the equation to solve for frequency:

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

Substituting the values:

\[
f = \frac{3.00 \times 10^8 \, \text{m/s}}{510 \times 10^{-9} \, \text{m}}
\]

Calculating this gives:

\[
f = \frac{3.00 \times 10^8}{510 \times 10^{-9}} \approx \frac{3.00 \times 10^8}{5.10 \times 10^{-7}} \approx 5.88 \times 10^{14} \, \text{Hz}
\]

When rounded to the nearest tenth and expressed in scientific notation, the frequency of green light is:

\[
f \approx 5.9 \times 10^{14} \, \text{Hz}
\]