Problem 10 - Chemistry and Chemical Reactivity

Question

Place the following types of radiation in order of increasing energy per photon. (a) radar signals (b) radiation within a microwave oven (c) gamma rays from a nuclear reaction (d) red light from a neon sign (c) ultraviolet radiation from a sun lamp

Step-by-Step Solution

Answer

Radar, microwave, red light, ultraviolet, gamma rays.

Step 1: Understanding the Concept of Energy per Photon

The energy of a photon is directly related to its frequency by the equation \( E = h \cdot f \), where \( E \) is the energy, \( h \) is Planck's constant, and \( f \) is the frequency. Thus, higher frequency radiation has more energy per photon.

Step 2: Identifying the Frequencies

To order the types of radiation, we identify their general frequencies: - Radar signals have the lowest frequencies among electromagnetic waves. - Microwaves are higher in frequency than radar signals but lower than infrared. - Photons in red light have even higher frequencies than microwaves. - Ultraviolet (UV) radiation has higher frequencies than visible light. - Gamma rays have the highest frequencies, much higher than UV radiation.

Step 3: Ordering the Types of Radiation

Order the types of radiation from lowest to highest frequency, which directly corresponds to increasing energy per photon: 1. Radar signals 2. Microwave oven radiation 3. Red light from a neon sign 4. Ultraviolet radiation from a sun lamp 5. Gamma rays from a nuclear reaction.

Key Concepts

Energy per Photon

The concept of energy per photon is a fascinating part of the electromagnetic spectrum. Every photon, or particle of light, carries energy determined by its frequency. The relationship between the energy and frequency of a photon is defined by the equation \( E = h \cdot f \), where \( E \) represents energy, \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} \, \text{Joule-second} \)), and \( f \) denotes frequency.

This equation means that the energy of a photon is directly proportional to its frequency. In simpler terms:

• A photon with a higher frequency will have more energy.
• This implies that different types of radiation, depending on their frequency, will carry different amounts of energy per photon.

This is crucial for understanding how different types of electromagnetic radiation such as visible light, microwaves, and gamma rays vary in energy levels.

Radiation Frequency

Radiation frequency is the number of wave cycles that pass a point per unit time, usually measured in Hertz (Hz). Frequency plays a crucial role in determining the energy of a photon. Higher frequencies mean more energy, while lower frequencies indicate less energy.

To get a clearer picture, here’s a brief overview of some radiation types and their typical frequencies:

• Radar Signals: These have some of the lowest frequencies in the electromagnetic spectrum.
• Microwaves: With frequencies higher than radar but lower than infrared, microwaves are commonly used in kitchen appliances.
• Red Light: This has frequencies that fall within the visible spectrum, higher than microwaves.
• Ultraviolet (UV) Radiation: UV types have frequencies higher than visible light, responsible for sunburns.
• Gamma Rays: These have extremely high frequencies, often resulting from nuclear reactions or radioactive decay.

Recognizing the frequency of each type of radiation helps us understand differences in photon energy across the spectrum.

Order of Radiation Types

The electromagnetic spectrum comprises various types of radiation, ordered by increasing frequency and, therefore, increasing energy per photon. To order these types, we start with the lowest energy and move up to the highest.

Here’s how different radiations stack up:

• Radar Signals: These come first with the lowest energy per photon, due to their low frequency.
• Microwave Oven Radiation: Next are microwaves, which have slightly higher frequency and energy than radar waves.
• Red Light from a Neon Sign: This falls within the visible spectrum and carries more energy per photon than microwaves.
• Ultraviolet Radiation from a Sun Lamp: With higher frequencies than visible light, UV radiation has more energy per photon.
• Gamma Rays from a Nuclear Reaction: Finally, gamma rays are at the top, with exceedingly high frequency and, thus, the most energy per photon.

Understanding this order showcases the diversity within the electromagnetic spectrum and highlights how energy levels vary with frequency.