Textbook Question
The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (d) What is the product of the decay process? [Section 21.4]
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Ch.21 - Nuclear Chemistry
Chapter 21, Problem 9
A sample of an alpha emitter having an activity of 0.18 Ci is stored in a 25.0-mL sealed container at 22 _x001D_C for 245 days. (b) Assuming that each alpha particle is converted to a helium atom, what is the partial pressure of helium gas in the container after this 245-day period?
Verified step by step guidance1
First, understand that the activity of the sample is given as 0.18 Ci (Curie), which is a measure of the number of disintegrations per second. Convert this activity into disintegrations per second using the conversion factor: 1 Ci = 3.7 x 10^10 disintegrations per second.
Next, calculate the total number of disintegrations over the 245-day period. Convert the time from days to seconds (1 day = 86400 seconds) and multiply by the disintegrations per second obtained in the previous step.
Assume that each disintegration results in the formation of one helium atom. Therefore, the total number of helium atoms formed is equal to the total number of disintegrations calculated.
Use the ideal gas law to find the partial pressure of helium gas. The ideal gas law is given by: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin. Convert the temperature from Celsius to Kelvin by adding 273.15.
Calculate the number of moles of helium using the total number of helium atoms and Avogadro's number (6.022 x 10^23 atoms/mol). Substitute the values for \( n \), \( V \), \( R \), and \( T \) into the ideal gas law equation to solve for the partial pressure \( P \) of helium gas in the container.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radioactive Decay
Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This decay occurs at a characteristic rate for each isotope, described by its half-life, which is the time required for half of the radioactive atoms in a sample to decay. Understanding this concept is crucial for calculating the amount of a radioactive substance remaining after a given time.
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03:00
Rate of Radioactive Decay
Activity and Units of Measurement
Activity refers to the rate at which a radioactive sample decays, typically measured in curies (Ci) or becquerels (Bq). One curie is defined as 3.7 x 10^10 disintegrations per second. Knowing the initial activity allows us to determine how many alpha particles are emitted over a specific time period, which is essential for calculating the resulting amount of helium gas produced.
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02:52Units of Radiation Measurement
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental for calculating the partial pressure of gases in a mixture. In this scenario, after determining the moles of helium produced from the decay, we can use the Ideal Gas Law to find the partial pressure of helium in the sealed container.
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01:15Ideal Gas Law Formula
Related Practice
Textbook Question
All the stable isotopes of boron, carbon, nitrogen, oxygen, and fluorine are shown in the accompanying chart (in red), along with their radioactive isotopes with t1>2 7 1 min (in blue). (b) Which radioactive isotopes are most likely to decay by beta emission? [Sections 21.2, 21.4, and 21.5]
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Textbook Question
Indicate the number of protons and neutrons in the following nuclei: (b) 193Tl.
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Textbook Question
Indicate the number of protons and neutrons in the following nuclei: (c) neptunium-237.
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