Magnetism and magnetic fields Study Guide

Radioactive decay is a random process where unstable atomic nuclei spontaneously transform into more stable ones, emitting radiation. The rate at which this occurs is measured by activity, often in becquerels (Bq), which represents the number of decays per second. A key concept in describing this decay is the half-life. The half-life of a radioactive isotope is the time it takes for half of the radioactive nuclei in a sample to decay, or equivalently, for the activity of the sample to halve.

When calculating the net decline, we are interested in how much the original amount (or activity) has decreased over a certain number of half-lives. This decline can be expressed as a ratio. For example, after one half-life, the remaining amount is 1/2 of the original. After two half-lives, it's (1/2) * (1/2) = 1/4 of the original. After three half-lives, it's (1/2) * (1/2) * (1/2) = 1/8 of the original. In general, after 'n' half-lives, the fraction remaining is (1/2)^n.

The net decline, when expressed as a ratio, describes how much of the original sample has decayed. If the fraction remaining is (1/2)^n, then the fraction that has decayed is 1 - (1/2)^n. We often express the decline as a ratio of the decayed amount to the original amount, or simply state the final remaining amount as a fraction or ratio relative to the initial. For instance, if 7/8 of a substance has decayed after three half-lives, the net decline in terms of the original amount is 7/8. Alternatively, the ratio of the original activity to the remaining activity could be calculated, which would be 1 / (1/2)^n or 2^n.

For example, if a sample undergoes 3 half-lives:

• After 1 half-life, 1/2 remains, 1/2 has decayed.
• After 2 half-lives, 1/4 remains, 3/4 has decayed.
• After 3 half-lives, 1/8 remains, 7/8 has decayed.

The 'net decline' could refer to the fraction that has decayed, or the ratio of initial to final, or final to initial. The question often specifies what ratio or fraction is required. If asked for the net decline as a ratio of original to remaining, after 'n' half-lives, the ratio would be 1 : (1/2)^n, which simplifies to 2^n : 1. If asked for the fraction that has decayed, it's 1 - (1/2)^n.

The electromagnetic (EM) spectrum is a continuous range of all possible electromagnetic waves, arranged according to their wavelength and frequency. All EM waves are transverse waves and travel at the same speed in a vacuum, which is the speed of light (approximately 3 x 10^8 metres per second). Despite this constant speed, different types of EM waves have distinct properties and applications, largely due to their differing wavelengths and frequencies. The spectrum is typically divided into several main groupings: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These groupings are not distinct categories with sharp boundaries but rather merge into one another. As you move along the spectrum from radio waves to gamma rays, the wavelength decreases, and consequently, the frequency increases. Wavelength and frequency are inversely proportional for all electromagnetic waves because their speed in a vacuum is constant. This relationship means that waves with longer wavelengths have lower frequencies, and waves with shorter wavelengths have higher frequencies. Understanding this organised structure allows us to appreciate the diverse ways in which EM radiation interacts with matter and is used in modern technology and medicine.