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Ch.20 - Radioactivity and Nuclear Chemistry
Tro - Chemistry: A Molecular Approach 4th Edition
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831당신이 사용하는 게 아니라요?교과서 변경
20장, 문제 96

The half-life of 235U, an alpha emitter, is 7.1⨉108 years. Calculate the number of alpha particles emitted by 1.0 mg of this nuclide in 1.0 minute.

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1
Determine the number of moles of 235U in 1.0 mg. Use the molar mass of 235U, which is approximately 235 g/mol.
Calculate the number of atoms of 235U using Avogadro's number (6.022 × 10^23 atoms/mol).
Use the half-life formula to find the decay constant (k) for 235U: k = \(\frac{\ln(2)}{\text{half-life}\)}.
Calculate the number of decays (and thus alpha particles emitted) in 1.0 minute using the formula: N = N_0 (1 - e^{-kt}), where N_0 is the initial number of atoms and t is the time in minutes.
Convert the time from minutes to years if necessary, and solve for the number of alpha particles emitted.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Half-life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. For uranium-235, which has a half-life of 7.1 × 10^8 years, this means that after this period, only half of the original amount of uranium-235 will remain, while the other half has transformed into other elements through radioactive decay.
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Zero-Order Half-life

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation, such as alpha particles. In the case of uranium-235, it decays by emitting alpha particles, which consist of two protons and two neutrons, effectively reducing the atomic number and mass of the original nucleus.
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Rate of Radioactive Decay

Activity and Emission Rate

The activity of a radioactive sample is defined as the number of decays per unit time, typically measured in becquerels (Bq). To calculate the number of alpha particles emitted by a sample, one can use the activity formula, which incorporates the number of radioactive atoms present and the decay constant derived from the half-life, allowing for the determination of emissions over a specified time frame.
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01:51
Emission Spectra