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Chapter 19: Problem 18

A Geiger counter counts \(0.070 \%\) of all particles emitted by a sample. What is the activity that registers \(19.4 \times 10^{3}\) counts in one minute?

Short Answer

Expert verified
Answer: The total activity of the sample is approximately 27,714,286 counts per minute.

Step by step solution

01

Identify the information given in the problem.

We are given the following information: - Geiger counter efficiency: 0.070% - Counts registered in one minute: 19.4 x 10^3
02

Calculate the actual percentage of counted particles

The efficiency of the Geiger counter is 0.070%. To find the actual percentage, we need to convert this value from percentage to a decimal value. To do that, divide 0.070% by 100: 0.070% = 0.0007 So, the actual percentage of counted particles is 0.0007.
03

Find the activity of the total particles emitted

Now that we know the Geiger counter only counts 0.0007 of the total particles, we can find the 100% equivalent to get the activity of the total particles emitted: Let X be the total activity of the sample: 0.0007 * X = 19.4 x 10^3 Now we need to solve for X: X = (19.4 x 10^3) / 0.0007
04

Calculate the total activity

Now that we have the equation set up, we can plug in the values and solve for X: X = (19.4 x 10^3) / 0.0007 X = 27714285.71
05

Present the result

The total activity that registers 19.4 x 10^3 counts in one minute by the Geiger counter is approximately 27,714,286 counts per minute.

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Most popular questions from this chapter

A \(100.0\) -g sample of water containing tritium, \({ }_{1}^{3} \mathrm{H}\), emits \(2.89 \times 10^{3}\) beta particles per second. Tritium has a half-life of \(12.3\) years. What percentage of all the hydrogen atoms in the water sample is tritium?

Consider the fission reaction $${ }_{0}^{1} n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{3}{ }_{3}^{89} \mathrm{Rb}+{ }_{55}^{144} \mathrm{Ce}+3_{-1}^{0} e+3{ }_{0}^{1} n$$ How many liters of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), the primary component of gasoline, must be burned to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) to produce as much energy as the fission of one gram of U-235 fuel? Octane has a density of \(0.703 \mathrm{~g} / \mathrm{mL} ;\) its heat of formation is \(-249.9 \mathrm{~kJ} / \mathrm{mol}\).

Which has the larger binding energy, fluorine- 19 or oxygen-17?

Lead-210 has a half-life of \(20.4\) years. This isotope decays by beta particle emission. A counter registers \(1.3 \times 10^{4}\) disintegrations in five minutes. How many grams of \(\mathrm{Pb}-210\) are there?

A scintillation counter registers emitted radiation caused by the disintegration of nuclides. If each atom of nuclide emits one count, what is the activity of a sample that registers \(3.00 \times 10^{4}\) disintegrations in five minutes?
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