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Chapter 42: Problem 66

A radiation detector records 8700 counts in 1.00 min. Assuming that the detector records all decays, what is the activity of the radiation source in (a) becquerels and (b) curies?

Short Answer

Expert verified
The activity is 145 Bq or 3.92 脳 10鈦烩伖 Ci.

Step by step solution

01

Understanding the Problem

The problem provides the total number of counts recorded by a radiation detector in one minute, which is 8700 counts. We assume that each count corresponds to a decay event and the detector is 100% efficient at recording these events. We need to calculate the activity of the radiation source in two different units: becquerels (Bq) and curies (Ci).
02

Convert Counts to Becquerels

One becquerel (Bq) is defined as one decay per second. Since the detector records exactly 8700 counts in one minute, we first convert the time to seconds: 1 minute = 60 seconds. Therefore, the activity in becquerels is the total counts divided by the time in seconds. This gives us:\[Activity (Bq) = \frac{8700 \text{ counts}}{60 \text{ s}} = 145 \text{ Bq}\]
03

Convert Becquerels to Curies

One curie (Ci) is equal to \(3.7 \times 10^{10}\) becquerels. To convert the activity from becquerels (145 Bq) to curies, we use the conversion factor between the two units:\[Activity (Ci) = \frac{145 \text{ Bq}}{3.7 \times 10^{10} \text{ Bq/Ci}}\]Performing the division gives us:\[Activity (Ci) = 3.919 \times 10^{-9} \text{ Ci}\]
04

Final Review and Verification

Ensure all calculations are correct and units are consistent. Confirm that the calculations follow the proper conversion factors:- Becquerel (Bq) is confirmed as decays per second.- Curie (Ci) is confirmed using the conversion \(1 \text{ Ci} = 3.7 \times 10^{10} \text{ Bq}\). Both conversions appear accurate.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Becquerel (Bq)
When referring to radioactive decay, a becquerel (Bq) is an essential unit of measurement. It measures the rate at which a radioactive source decays, where one Bq equals one disintegration or decay per second.
This simple measurement helps scientists and engineers determine how active a particular radioactive source is. By knowing the activity of a source, they can predict how fast it will emit radiation over time.
The becquerel is a standard unit of the International System of Units (SI), making it widely used in scientific calculations and discussions. Given this, when we see an activity reading such as 145 Bq, it means the radioactive source experiences 145 decay events every second.
  • One Bq = One decay per second
  • SI unit for radioactivity
  • Used in scientific and engineering applications
Exploring Curie (Ci)
The curie (Ci) is another unit used to measure radioactivity. Historically, it's based on the activity of one gram of radium-226, which was originally used as a standard for measuring radiation.
One curie is much larger than one becquerel, being equivalent to 3.7 x 10^10 decays per second or 3.7 x 10^10 Bq.
Despite not being an SI unit, the curie is still widely used, especially in the medical and nuclear industries. It's an excellent unit when dealing with large amounts of radioactive material.
To put it into perspective, when we calculate an activity of a mere 3.919 x 10^-9 Ci, it indicates a comparatively low level of radioactivity, as it's significantly smaller than the standard defined by the curie.
  • 1 Ci = 3.7 x 10^10 Bq
  • Used for large radiation measurements
  • Common in medical and nuclear fields
Radiation Detection Techniques
Detecting radiation involves using devices that can measure and quantify radioactive decay. These devices, known as radiation detectors, work by capturing the decay events from a radioactive source.
Different types of detectors are used based on the specific needs of measurement, including
  • Geiger-M眉ller tubes: Often used for detecting ionizing radiation
  • Scintillation counters: Efficient at measuring alpha, beta, and gamma radiation
  • Semiconductor detectors: Highly accurate, used in professional applications

These detectors convert physical decay events into electrical signals or "counts", which are then interpreted to quantify the radioactivity. In exercises such as interpreting 8700 counts per minute, these instruments help us determine activity levels in Bq or Ci depending on the need of the situation.
By understanding their functioning and applications, students can appreciate how critical these tools are for ensuring safety and precision in fields involving radioactive materials.

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Most popular questions from this chapter

The half-life of a particular radioactive isotope is \(6.5 \mathrm{~h}\). If there are initially \(48 \times 10^{19}\) atoms of this isotope, how many remain at the end of \(26 \mathrm{~h}\) ?

The isotope \({ }^{238} \mathrm{U}\) decays to \({ }^{206} \mathrm{~Pb}\) with a half-life of \(4.47 \times 10^{9} \mathrm{y}\). Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead. That is, $${ }^{238} \mathrm{U} \rightarrow{ }^{206} \mathrm{~Pb}+\text { various decay products. }$$ A rock is found to contain \(4.20 \mathrm{mg}\) of \({ }^{238} \mathrm{U}\) and \(2.135 \mathrm{mg}\) of \({ }^{206} \mathrm{~Pb}\). Assume that the rock contained no lead at formation, so all the lead now present arose from the decay of uranium. How many atoms of (a) \({ }^{238} \mathrm{U}\) and (b) \({ }^{206} \mathrm{~Pb}\) does the rock now contain? (c) How many atoms of \({ }^{238} \mathrm{U}\) did the rock contain at formation? (d) What is the age of the rock?

The cesium isotope \({ }^{137} \mathrm{Cs}\) is present in the fallout from aboveground detonations of nuclear bombs. Because it decays with a slow \((30.2 \mathrm{y})\) half-life into \({ }^{137} \mathrm{Ba},\) releasing considerable energy in the process, it is of environmental concern. The atomic masses of the Cs and \(\mathrm{Ba}\) are 136.9071 and \(136.9058 \mathrm{u},\) respectively; calculate the total energy released in such a decay.

Under certain rare circumstances, a nucleus can decay by emitting a particle more massive than an alpha particle. Consider the decays $${ }^{223} \mathrm{Ra} \rightarrow{ }^{209} \mathrm{~Pb}+{ }^{14} \mathrm{C} \quad \text { and } \quad{ }^{223} \mathrm{Ra} \rightarrow{ }^{219} \mathrm{Rn}+{ }^{4} \mathrm{He}$$ Calculate the \(Q\) value for the (a) first and (b) second decay and determine that both are energetically possible. (c) The Coulomb barrier height for alpha-particle emission is \(30.0 \mathrm{MeV}\). What is the barrier height for \({ }^{14} \mathrm{C}\) emission? (Be careful about the nuclear radii.) The needed atomic masses are $$ \begin{aligned} &\begin{array}{llll} { }^{223} \mathrm{Ra} & 223.01850 \mathrm{u} & { }^{14} \mathrm{C} & 14.00324 \mathrm{u} \end{array}\\\ &{ }^{209} \mathrm{~Pb} \quad 208.98107 \mathrm{u} \quad{ }^{4} \mathrm{He} \quad 4.00260 \mathrm{u}\\\ &{ }^{219} \mathrm{Rn} \quad 219.00948 \mathrm{u} \end{aligned} $$

What is the binding energy per nucleon of the americium isotope \({ }_{95}^{244} \mathrm{Am} ?\) Here are some atomic masses and the neutron mass. $$\begin{array}{lr}{ }_{95}^{244} \mathrm{Am} & 244.064279 \mathrm{u} \\\\\mathrm{n} & 1.008665 \mathrm{u}\end{array} { }^{1} \mathrm{H} \quad 1.007825 \mathrm{u}$$
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