Question

List these three types of electromagnetic radiation-visible, gamma rays, and microwaves-in order of: (a) decreasing energy per photon (b) decreasing frequency (c) decreasing wavelength

Short answer

a) Gamma rays, visible light, microwaves. b) Gamma rays, visible light, microwaves. c) Microwaves, visible light, gamma rays.

Step-by-step solution

Understanding Electromagnetic Spectrum

Electromagnetic radiation can be characterized by its energy, frequency, and wavelength. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is described by the equations: \( E = h u \) and \( c = u \lambda \), where \( E \) is energy, \( h \) is Planck's constant, \( u \) (nu) is frequency, \( c \) is the speed of light, and \( \lambda \) (lambda) is wavelength.

Ordering by Decreasing Energy Per Photon

To order the types of electromagnetic radiation by decreasing energy per photon, recall that gamma rays have the highest frequency (and hence energy), followed by visible light, and then microwaves. As energy and frequency are directly related, the order will be same for both energy and frequency.

Ordering by Decreasing Frequency

Following the relationship between energy and frequency, the electromagnetic radiation will be ordered as gamma rays, visible light, and microwaves.

Ordering by Decreasing Wavelength

Since wavelength is inversely related to both energy and frequency, to order them by decreasing wavelength, we simply reverse the order of increasing energy or frequency. The order will be microwaves, visible light, and gamma rays.

Key concepts

Energy Per Photon

Understanding the concept of energy per photon is fundamental in the study of electromagnetic radiation. Photons are particles of light, and each carries a discrete amount of energy. This energy is determined by the equation:
\[ E = hu \]
where \( E \) represents the energy of the photon, \( h \) is Planck's constant (approximately \(6.626 \times 10^{-34}\) Joule seconds), and \( u \) (nu) is the frequency of the radiation. Planck's constant is a very small number, which tells us that the energy carried by photons is also quite tiny.

What stands out in this relationship is that the energy of a photon increases as the frequency increases. Hence, when listing types of electromagnetic radiation like gamma rays, visible light, and microwaves in terms of decreasing energy per photon, we also inherently list them in decreasing frequency. Gamma rays sit at the top with the highest energy photons, followed by visible light, and with microwaves having the least energetic photons among the three. It’s crucial to note that even though these energies are very small, they have significant effects on the atomic and molecular level.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, and each type is distinguished by its wavelength. At one extreme of the spectrum, you have gamma rays with the shortest wavelengths, and at the other end, you have radio waves with the longest wavelengths.

Different regions of the electromagnetic spectrum are used in various technologies. For example, microwaves are used for communication and cooking food, visible light is, of course, the part we see with our eyes, and gamma rays are used in medical treatments and are produced in high-energy astronomical phenomena.

Each type of electromagnetic radiation fits into a place on the spectrum according to its wavelength and frequency, creating a wide array of electromagnetic waves that have various applications and effects in the world. It also is reflective of the diversity in energy per photon among different electromagnetic waves, influencing how we utilize and protect against different types of radiation in daily life.

Wavelength and Frequency Relationship

Wavelength (\( \lambda \)) and frequency (\( u \)) of electromagnetic waves are inversely proportional to each other. This intrinsic relationship ties together with the speed of light (\( c \)), via the equation:
\[ c = \lambdau \]
where \( c \) is the constant speed of light in a vacuum, approximately \(3 \times 10^8\) meters per second. This means that as the frequency of an electromagnetic wave increases, its wavelength decreases, and vice versa.

For example, when we order the types of electromagnetic radiation by decreasing wavelength, we are simultaneously ordering them by increasing frequency and energy per photon. This is because the longer the wavelength, the lower the frequency, and thus the lower the energy. Microwaves have a long wavelength compared to visible light and gamma rays, placing them lower in frequency and energy on the electromagnetic spectrum.

Understanding this relationship is crucial for many practical applications, such as satellite communication, where frequency allocations are made based on the wavelength of the radiation to avoid signal interference and to utilize the electromagnetic spectrum efficiently.