Question

What is the wavelength of a light if the frequency is 2.33 x 10 17 cycles/second (Hz)?
a. What is the type of electromagnetic radiation? Look at the chart above.
4. 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, we can use the formula that relates wavelength (\(\lambda\)), frequency (\(f\)), and the speed of light (\(c\)):

\[
c = \lambda f
\]

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

### 1. Wavelength Calculation for the First Frequency

Given:
- Frequency (\(f\)) = \(2.33 \times 10^{17}\) Hz

Rearranging the formula to solve for wavelength gives us:

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

Now, substituting in the values:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{2.33 \times 10^{17} \, \text{Hz}} \approx 1.29 \times 10^{-9} \, \text{m} = 1.29 \, \text{nm}
\]

### Type of Electromagnetic Radiation

A wavelength of approximately 1.29 nm falls within the ultraviolet (UV) region of the electromagnetic spectrum.

### 2. Wavelength Calculation for the Sodium Yellow Light

Given:
- Frequency (\(f\)) = \(5.0 \times 10^{14}\) Hz

Using the same formula for wavelength:

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

Substituting in the values:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{5.0 \times 10^{14} \, \text{Hz}} \approx 6.00 \times 10^{-7} \, \text{m} = 600 \, \text{nm}
\]

### Summary of Results
1. The wavelength for the frequency \(2.33 \times 10^{17}\) Hz is approximately **1.29 nm** (UV radiation).
2. The wavelength for the yellow light from sodium with frequency \(5.0 \times 10^{14}\) Hz is approximately **600 nm** (visible light).