Question

What is the frequency of a photon of light when it has a wavelength of 4.55 x 10 -7 m?

Answer 1

To find the frequency of a photon when its wavelength is known, you can use the wave equation:

\[
c = \lambda \cdot f
\]

where:
- \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength (in meters),
- \( f \) is the frequency (in Hertz).

Rearranging the equation to solve for frequency gives:

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

Substituting in the given values:

- \( c = 3.00 \times 10^8 \) m/s
- \( \lambda = 4.55 \times 10^{-7} \) m

Now, we can calculate \( f \):

\[
f = \frac{3.00 \times 10^8 \, \text{m/s}}{4.55 \times 10^{-7} \, \text{m}}
\]

Calculating this gives:

\[
f \approx \frac{3.00 \times 10^8}{4.55 \times 10^{-7}} \approx 6.59 \times 10^{14} \, \text{Hz}
\]

Thus, the frequency of the photon of light with a wavelength of \( 4.55 \times 10^{-7} \) m is approximately \( 6.59 \times 10^{14} \) Hz.