Question

A bright yellow light from the emission spectrum of sodium has a frequency of 5.0 x 10 14
cycles/second (Hz). What is the wavelength of this yellow light?

Answer 1

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

\[
c = \lambda \cdot f
\]

Where:
- \( c \) is the speed of light, approximately \( 3.0 \times 10^8 \) meters per second (m/s),
- \( f \) is the frequency in hertz (Hz),
- \( \lambda \) is the wavelength in meters (m).

We can rearrange this formula to solve for wavelength \( \lambda \):

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

Given:
- \( f = 5.0 \times 10^{14} \) Hz,
- \( c = 3.0 \times 10^8 \) m/s.

Now we can plug in the values:

\[
\lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{5.0 \times 10^{14} \, \text{Hz}}
\]

Calculating this gives:

\[
\lambda = \frac{3.0}{5.0} \times \frac{10^8}{10^{14}} = 0.6 \times 10^{-6} \text{ m}
\]

Thus, converting \( 0.6 \times 10^{-6} \, \text{m} \) to nanometers (1 m = \( 10^9 \) nm):

\[
\lambda = 0.6 \times 10^{-6} \text{ m} \times 10^9 \text{ nm/m} = 600 \text{ nm}
\]

Therefore, the wavelength of the yellow light is approximately **600 nm**.