Open Question
The overall hydrogen burning reaction in stars can be represented as the conversion of four protons to one alpha particle. Use the data for the mass of H-1 and He-4 to calculate the energy released by this process.
Ch.20 - Radioactivity and Nuclear Chemistry
Chapter 20, Problem 91
The half-life of 238U is 4.5⨉109 yr. A sample of rock of mass 1.6 g produces 29 dis/s. Assuming all the radioactivity is due to 238U, find the percent by mass of 238U in the rock.
Verified step by step guidance1
Determine the decay constant (\( \lambda \)) using the half-life formula: \( \lambda = \frac{\ln(2)}{t_{1/2}} \), where \( t_{1/2} = 4.5 \times 10^9 \) years.
Convert the decay constant from per year to per second by using the conversion factor: 1 year = 3.15 \times 10^7 seconds.
Use the decay rate formula \( A = \lambda N \) to find the number of \( ^{238}U \) atoms (\( N \)) in the sample, where \( A = 29 \) disintegrations per second.
Calculate the mass of \( ^{238}U \) using the number of atoms \( N \) and Avogadro's number (\( 6.022 \times 10^{23} \) atoms/mol), along with the molar mass of \( ^{238}U \) (238 g/mol).
Determine the percent by mass of \( ^{238}U \) in the rock by dividing the mass of \( ^{238}U \) by the total mass of the rock (1.6 g) and multiplying by 100.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Half-life
Half-life is the time required for half of the radioactive nuclei in a sample to decay. For uranium-238, this period is approximately 4.5 billion years. Understanding half-life is crucial for calculating the remaining quantity of a radioactive isotope in a sample over time, which is essential for determining the mass percentage of uranium-238 in the rock.
Recommended video:
Guided course
02:17
Zero-Order Half-life
Radioactivity and Decay Rate
Radioactivity refers to the process by which unstable atomic nuclei lose energy by emitting radiation. The decay rate, measured in disintegrations per second (dis/s), indicates how many atoms decay in a given time frame. In this problem, the decay rate of 29 dis/s provides the necessary information to calculate the amount of uranium-238 present in the rock sample.
Recommended video:
Guided course
03:00Rate of Radioactive Decay
Mass Percent Calculation
Mass percent is a way to express the concentration of a component in a mixture, calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100. To find the percent by mass of uranium-238 in the rock, one must first determine the mass of uranium-238 based on its decay rate and then use the total mass of the rock sample to compute the percentage.
Recommended video:
Guided course
00:38Mass Percent Calculation
Related Practice
Textbook Question
The nuclide 247Es can be made by bombardment of 238U in a reaction that emits five neutrons. Identify the bombarding particle.
601
views
1
rank
Textbook Question
The nuclide 6Li reacts with 2H to form two identical particles. Identify the particles.
666
views
Textbook Question
The half-life of 232Th is 1.4⨉1010 yr. Find the number of disintegrations per hour emitted by 1.0 mol of 232Th.
762
views
1
comments
Open Question
A 1.50-L gas sample at 745 mm Hg and 25.0 °C contains 3.55% radon-220 by volume. Radon-220 is an alpha emitter with a half-life of 55.6 s. How many alpha particles are emitted by the gas sample in 5.00 minutes?
Open Question
A 228-mL sample of an aqueous solution contains 2.35% MgCl2 by mass. Exactly one-half of the magnesium ions are Mg-28, a beta emitter with a half-life of 21 hours. What is the decay rate of Mg-28 in the solution after 4.00 days? (Assume a density of 1.02 g/mL for the solution.)