Problem 10 - Chemistry and Chemical Reactivity

Question

Place the following types of radiation in order of increasing energy per photon: (a) radiation within a microwave oven (b) your favorite radio station (c) gamma rays from a nuclear reaction (d) red light from a neon sign (e) ultraviolet radiation from a sun lamp

Step-by-Step Solution

Answer

Radio station < Microwave oven < Red light < Ultraviolet < Gamma rays.

Step 1: Understanding Radiation Types

Different types of radiation have different energies per photon. The energy of a photon is related to its frequency, with higher frequencies corresponding to higher energies.

Step 2: Identifying Frequencies

In the electromagnetic spectrum, common frequencies from largest to smallest are: (a) Radio waves, which are used for radio broadcasts (b) Microwaves, used in microwave ovens (c) Infrared waves, such as red light (d) Ultraviolet rays (e) Gamma rays.

Step 3: Ordering According to Energy

Since energy per photon is directly proportional to frequency, we order the radiation types as follows from lowest energy to highest: (b) Radio waves < (a) Microwaves < (d) Red light < (e) Ultraviolet < (c) Gamma rays.

Step 4: Final Order

Thus, in terms of increasing energy per photon, the order is: 1. Radio station 2. Microwave oven 3. Red light 4. Ultraviolet radiation 5. Gamma rays.

Key Concepts

Photon Energy

Photon energy is a core concept in understanding the electromagnetic spectrum. Each photon, depending on its type of radiation, carries a specific amount of energy. Understanding this concept is crucial because it's the energy of the photon that determines its characteristics and applications. The photon energy (\( E \)) is calculated using the equation:\[ E = h u \]where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Js) and \( u \) is the frequency of the radiation in hertz (Hz). Since energy is directly proportional to frequency, higher frequencies lead to higher photon energies.
Different types of radiation, from radio waves to gamma rays, have varying photon energies. Lower frequency waves like radio waves have low photon energy. On the other hand, high-frequency waves such as gamma rays have high photon energies. Understanding these relationships helps us explain phenomena like why gamma rays are highly penetrating and potentially damaging.

Frequency and Wavelength

Frequency and wavelength are two key properties of waves in the electromagnetic spectrum. They are inversely related: as one increases, the other decreases. This relationship can be defined by the equation:\[ c = \lambda u \]where \( \lambda \) is the wavelength, \( u \) is the frequency, and \( c \) is the speed of light (\( 3 \times 10^{8} \) m/s).

• A longer wavelength means a lower frequency and thus lower photon energy.
• A shorter wavelength means a higher frequency and thus higher photon energy.

By knowing the frequency, you can also determine how much energy a photon carries. For example, red light has a longer wavelength compared to ultraviolet light, which means it has a lower frequency and lower energy. This is why ultraviolet light can cause sunburns while visible red light does not. Frequency and wavelength are crucial for determining the place of each type of radiation within the electromagnetic spectrum.

Types of Radiation

The electromagnetic spectrum consists of a range of radiation types, each with distinct frequencies and energies. This spectrum extends from radio waves, which have the lowest energy, to gamma rays, which have the highest.

• Radio Waves: Used in communication systems like radio and TV. They have the lowest frequency and longest wavelength.
• Microwaves: Found in microwave ovens; they have a higher frequency than radio waves but still relatively low energy.
• Infrared Waves: Felt as heat; over red light on the spectrum and just below visible light.
• Visible Light: The only part of the spectrum visible to the human eye with red having the least energy in this part.
• Ultraviolet Light: Higher frequency than visible light; can cause skin tanning or burns.
• Gamma Rays: Emitted in nuclear reactions; highest frequency and photon energy, making them very penetrating.

The types of radiation in order of increasing energy per photon are radio waves, microwaves, infrared, visible light, ultraviolet, and finally, gamma rays. Each type of radiation has its specific use in technology and science based on its photon energy and frequency characteristics.