Problem 25 - Chemistry The Science in Context

Question

A neon light emits radiation of \(\lambda=616 \mathrm{nm} .\) What is the frequency of this radiation?

Step-by-Step Solution

Answer

Answer: The frequency of the radiation emitted by the neon light is approximately \(4.87 × 10^{14} Hz\).

Step 1: Convert the wavelength to meters

First, we need to convert the given wavelength from nanometers to meters. 1 nm = \(10^{-9}\) meters. So, λ = \(616 × 10^{-9} m\)

Step 2: Use the formula \(c = λf\) to calculate the frequency

We can use the formula \(c=λf\) where \(c\) is the speed of light, \(λ\) is the wavelength, and \(f\) is the frequency. We have the values for \(c\) and \(λ\), so we can now solve for the frequency \(f\). \(c = \lambda f\) Rearranging the formula to find \(f\), we get: \(f = \frac{c}{\lambda}\)

Step 3: Plug in the values and calculate the frequency

We have the values for \(c\) and \(λ\), so we can now calculate the frequency. \(f = \frac{3 × 10^8 m/s}{616 × 10^{-9} m}\)

Step 4: Simplify and find the answer

Now, we will perform the calculation to find the frequency of the radiation emitted by the neon light. \(f = \frac{3 × 10^8 m/s}{616 × 10^{-9} m} = \frac{3 × 10^8}{616 × 10^{-9}} = \frac{3 × 10^8}{6.16 × 10^{-7}}\) \(f \approx 4.87 × 10^{14} Hz\) So, the frequency of the radiation emitted by the neon light is approximately \(4.87 × 10^{14} Hz\).

Key Concepts

Speed of Light

The speed of light is a fundamental constant in the universe, signifying the fastest speed at which light and all other forms of electromagnetic radiation can travel in a vacuum. Denoted by the symbol 'c', the speed of light is approximately equal to 299,792,458 meters per second, or about 3 x 10^8 m/s in scientific notation.

Understanding the speed of light is crucial for a variety of physical laws and theories, including Einstein's theory of relativity, which reveals how the perception of time changes at speeds approaching 'c'. In the context of wavelength to frequency conversion, the speed of light serves as a bridge between the physical dimensions of waves and their time-related properties.

Electromagnetic Radiation

Electromagnetic radiation refers to waves of the electromagnetic field, propagating through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These types of radiation differ in wavelength, and consequently, in their frequency and energy.

The concept of electromagnetic radiation is essential when examining the nature of light and other forms of radiation as both wave-like and particle-like phenomena. In the context of frequency calculation, it's necessary to understand that each color of visible light has a specific wavelength range. When we talk about a neon light emitting radiation at a wavelength of 616 nm, we are referring to the characteristic color of light that corresponds to that wavelength within the electromagnetic spectrum.

Frequency Calculation

The frequency of a wave is the number of cycles it undergoes in one second, expressed in Hertz (Hz). Calculating frequency is an essential aspect of understanding wave phenomena and their interactions with matter.

When converting wavelength to frequency, we use the formula f = c/λ, where 'c' represents the speed of light, 'λ' is the wavelength, and 'f' is the frequency being calculated. Once the wavelength is measured in meters, the formula facilitates a direct calculation of the frequency of the electromagnetic wave. For a neon light with a wavelength of 616 nm, after converting to meters and applying the speed of light in the formula, one can deduce that its frequency is approximately 4.87 x 10^14 Hz.