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Chapter 40: Problem 8

What is more dangerous, a radioactive material with a short half-life or a long one?

Short Answer

Expert verified
Answer: The danger of radioactive materials with short or long half-lives depends on various factors, such as the type of radiation emitted, activity level, human exposure, and environmental impact. Short half-life materials may be more dangerous in the short-term due to their intense radiation release, while long half-life materials can pose long-term risks to humans and the environment. It is crucial to consider the specific context, exposure, and type of radiation involved to accurately determine which one is more dangerous.

Step by step solution

01

Introduction to Half-Life

Half-life is the time it takes for half of a sample of a radioactive material to decay. In other words, after one half-life, there will be half as much radioactive material as there was initially.
02

Short Half-Life

A radioactive material with a short half-life undergoes radioactive decay at a faster rate. This means that it would release a larger amount of radiation in a shorter period of time. As a result, materials with short half-lives can be more dangerous in certain situations, such as in close proximity to humans or other living organisms.
03

Long Half-Life

A radioactive material with a long half-life decays at a slower rate, and therefore releases radiation more slowly over time. Though the radiation emitted might be less intense than that of a short half-life material, it can still pose a significant danger due to its persistence in the environment. Materials with long half-lives can contaminate soil, water, air, and pose a long-term threat to humans, animals, and plants.
04

Factors Influencing Danger Levels

There are several factors to consider when assessing the danger posed by radioactive materials, some of which include: 1. The type of radiation emitted (alpha, beta, gamma, or neutron): Different types of radiation have varying levels of penetration and biological damage potential. 2. The activity level of the material: This refers to the number of radioactive decays occurring per unit time. Higher activity levels generally result in greater radiation exposure. 3. Human exposure: The danger of a radioactive material depends on how close a person is to the source, how long they are exposed, and what protective measures are in place. 4. Environmental impact: Long-lived radioactive materials can have a lasting impact on ecosystems and contribute to long-term contamination.
05

Conclusion

In conclusion, determining whether a radioactive material with a short half-life or a long one is more dangerous depends on various factors. A short half-life material may be more dangerous in the short-term due to high radiation intensity, while a long half-life material can pose long-term risks to both humans and the environment. It is crucial to consider the specific context, exposure, and type of radiation involved to make an accurate comparison.

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Most popular questions from this chapter

Calculate the binding energy for the following two uranium isotopes: a) \({ }_{92}^{238} \mathrm{U},\) which consists of 92 protons, 92 electrons, and 146 neutrons, with a total mass of \(238.0507826 \mathrm{u}\). b) \({ }^{235} \mathrm{U},\) which consists of 92 protons, 92 electrons, and 143 neutrons, with a total mass of \(235.0439299 \mathrm{u} .\) The atomic mass unit \(\mathrm{u}=1.66 \cdot 10^{-27} \mathrm{~kg} .\) Which isotope is more stable (or less unstable)?

The Sun radiates energy at the rate of \(3.85 \cdot 10^{26} \mathrm{~W}\) a) At what rate, in \(\mathrm{kg} / \mathrm{s}\), is the Sun's mass converted into energy? b) Why is this result different from the rate calculated in Example \(40.6,6.02 \cdot 10^{11}\) kg protons being converted into helium each second? c) Assuming that the current mass of the Sun is \(1.99 \cdot 10^{30} \mathrm{~kg}\) and that it radiated at the same rate for its entire lifetime of \(4.50 \cdot 10^{9} \mathrm{yr}\), what percentage of the Sun's mass was converted into energy during its entire lifetime?

The most common isotope of uranium, \({ }_{92}^{238} \mathrm{U},\) produces radon \({ }_{86}^{222} \mathrm{Rn}\) through the following sequence of decays: $$\begin{array}{c}{ }^{238} \mathrm{U} \rightarrow{ }^{234} \mathrm{Th}+\alpha,{ }^{234} \mathrm{Th} \rightarrow{ }^{234} \mathrm{~Pa}+\beta^{-}+\bar{\nu}_{e}, \\\\{ }_{91}^{234} \mathrm{~Pa} \rightarrow{ }_{92}^{234} \mathrm{U}+\beta+\bar{\nu}_{e},{ }^{234} \mathrm{U} \rightarrow{ }^{230} \mathrm{Th}+\alpha ,\\\\{ }_{91}^{230} \mathrm{Th} \rightarrow{ }_{90}^{226} \mathrm{Ra}+\alpha,{ }_{88}^{226} \mathrm{Ra} \rightarrow{ }_{86}^{222} \mathrm{Rn}+\alpha,\end{array}$$. A sample of \({ }_{92}^{238} \mathrm{U}\) will build up equilibrium concentrations of its daughter nuclei down to \({ }_{88}^{226} \mathrm{Ra} ;\) the concentrations of each are such that each daughter is produced as fast as it decays. The \({ }_{88}^{226} \mathrm{Ra}\) decays to \({ }_{86}^{222} \mathrm{Rn},\) which escapes as a gas. (The \(\alpha\) particles also escape, as helium; this is a source of much of the helium found on Earth.) In high concentrations, the radon is a health hazard in buildings built on soil or foundations containing uranium ores, as it can be inhaled. a) Look up the necessary data, and calculate the rate at which \(1.00 \mathrm{~kg}\) of an equilibrium mixture of \({ }_{92}^{238} \mathrm{U}\) and its first five daughters produces \({ }_{86}^{222} \mathrm{Rn}\) (mass per unit time). b) What activity (in curies per unit time) of radon does this represent?

Determine the decay constant of radium- 226 , which has a half-life of \(1600 \mathrm{yr}\).

Consider the Bethe-Weizsäcker formula for the case of odd \(A\) nuclei. Show that the formula can be written as a quadratic in \(Z\) -and thus, that for any given \(A\), the binding energies of the isotopes having that \(A\) take a quadratic form, \(B=a+b Z+c Z^{2} .\) Find the most deeply bound isotope (the most stable one) having \(A=117\) using your result.
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