What is the wavelength of a light if the frequency is 2.33 x 10 17 cycles/second (Hz)?

Question

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).