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Ch.21 - Nuclear Chemistry
Brown - Chemistry: The Central Science 14th Edition
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Tutti i libri di testoBrown 14th EditionCh.21 - Nuclear ChemistryProblema 36
Capitolo 21, Problema 36

It takes 4 h 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. What is the half-life of radium-230?

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Identify the initial mass \( m_0 = 2.00 \text{ mg} \) and the final mass \( m = 0.25 \text{ mg} \).
Note the time taken for this decay is 4 hours and 39 minutes, which needs to be converted to minutes: \( 4 \times 60 + 39 = 279 \text{ minutes} \).
Use the first-order decay formula: \( m = m_0 \times \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} \), where \( t \) is the time elapsed and \( t_{1/2} \) is the half-life.
Rearrange the formula to solve for the half-life \( t_{1/2} \): \( t_{1/2} = \frac{t}{\log_2\left(\frac{m_0}{m}\right)} \).
Substitute the known values into the equation to find \( t_{1/2} \).

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Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process occurs at a predictable rate for each radioactive isotope, characterized by its half-life, which is the time required for half of the radioactive atoms in a sample to decay.
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Rate of Radioactive Decay

Half-Life

Half-life is a specific measure of the time it takes for half of a given quantity of a radioactive substance to decay. It is a constant for each isotope and is crucial for calculating the remaining quantity of the substance over time, as well as for understanding the decay process in nuclear chemistry.
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Zero-Order Half-life

Exponential Decay Formula

The exponential decay formula describes how the quantity of a radioactive substance decreases over time. It is expressed as N(t) = N0 * (1/2)^(t/T), where N(t) is the remaining quantity at time t, N0 is the initial quantity, and T is the half-life. This formula allows for the calculation of remaining mass after a certain period, which is essential for solving decay problems.
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Beta Decay
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