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Chapter 19: Problem 15

A source for gamma rays has an activity of 3175 Ci. How many disintegrations are there for this source per minute?

Short Answer

Expert verified
Answer: Approximately 7.0485 × 10^14 disintegrations/min.

Step by step solution

01

Write down the given activity in curies

The given activity of the gamma-ray source in curies is 3175 Ci.
02

Convert the activity from curies to disintegrations per second using the conversion factor

Using the conversion factor (1 Ci = 3.7 × 10^10 disintegrations per second), let's convert the activity to disintegrations per second: (3175 \, \text{Ci}) \times (3.7 \times 10^{10} \, \text{disintegrations/s})/(\text{Ci}) = 1.17475 \times 10^{13} \, \text{disintegrations/s}.
03

Convert the disintegrations per second to disintegrations per minute

Now, we'll convert from disintegrations per second to disintegrations per minute, knowing that there are 60 seconds in a minute: (1.17475 \times 10^{13} \, \text{disintegrations/s}) \times (60 \, \text{s})/(\text{min}) = 7.0485 \times 10^{14} \, \text{disintegrations/min}.
04

State the final answer

The number of disintegrations for this gamma-ray source per minute is approximately 7.0485 × 10^14 disintegrations/min.

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Most popular questions from this chapter

An activity of 20 picocuries \(\left(20 \times 10^{-12} \mathrm{Ci}\right)\) of radon- 222 per liter of air in a house constitutes a health hazard to anyone living there. The half-life of radon-222 is \(3.82\) days. Calculate the concentration of radon in air (moles per liter) that corresponds to a 20-picocurie activity level.

A sample of a wooden artifact gives \(5.0\) disintegrations \(/ \mathrm{min} / \mathrm{g}\) carbon. The half-life of carbon-14 is 5730 years, and the activity of C-14 in wood just cut down from a tree is \(15.3\) disintegrations \(/ \mathrm{min} / \mathrm{g}\) carbon. How old is the wooden artifact?

An explosion used five tons \((1\) ton \(=2000 \mathrm{lb}\) ) of ammonium nitrate \((\Delta E=-37.0 \mathrm{~kJ} / \mathrm{mol})\). (a) How much energy was released by the explosion? (b) How many grams of TNT \((\Delta E=-2.76 \mathrm{~kJ} / \mathrm{g})\) are needed to release the energy calculated in (a)? (c) How many grams of U-235 are needed to obtain the same amount of energy calculated in (a)? (See the equation in Problem 45.)

Write balanced nuclear equations for the bombardment of (a) U-238 with a nucleus to produce Fm-249 and five neutrons. (b) Al-26 with an alpha particle to produce P-30. (c) Cu-63 with a nucleus producing \(\mathrm{Zn}-63\) and a neutron. (d) Al-27 with deuterium \(\left({ }_{1}^{2} \mathrm{H}\right)\) to produce an alpha particle and another nucleus.

Cobalt-60 is used extensively in medicine as a source of \(\gamma\) -rays. Its half-life is \(5.27\) years. (a) How long will it take a \(\mathrm{Co}-60\) source to decrease to \(18 \%\) of its original activity? (b) What percent of its activity remains after 29 months?
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