You want to find out how many atoms of the isotope 65 Cu are in a small sample of material. You

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You want to find out how many atoms of the isotope 65 Cu are...

You want to find out how many atoms of the isotope 65 $\mathrm{Cu}$ are in a small sample of material. You bombard the sample with neutrons to ensure that on the order of 1$\%$ of these copper nuclei absorb a neutron. After activation, you turn off the neutron flux and then use a highly efficient detector to monitor the gamma radiation that comes out of the sample. Assume half of the 66 $\mathrm{Cu}$ nuclei emit a 1.04 -MeV gamma ray in their decay. (The other half of the activated nuclei decay directly to the ground state of $66 \mathrm{Ni} . )$ If after 10 $\mathrm{min}$ (two half-lives) you have detected $10^{4}$ MeV of photon energy at 1.04 MeV, (a) approximately how many 65 $\mathrm{Cu}$ atoms are in the sample? (b) Assume the sample contains natural copper. Refer to the isotopic abundances listed in Table 44.2 and estimate the total mass of copper in the sample.

Key Concepts

Isotopic Abundance and Mass Estimation

Isotopic abundance refers to the relative amounts of different isotopes present in a natural element. By combining the measured number of atoms of a particular isotope (found through neutron activation and gamma detection) with natural abundance data, one can estimate the total mass of the element in the sample.

Branching Ratios and Decay Schemes

Branching ratios indicate the fraction of decays that follow different decay modes. Understanding these ratios is essential for converting the detected gamma-ray signal into the number of decaying nuclei, especially when only a portion of the decays produce gamma rays of a specific energy.

Half-Life and Radioactive Decay

The half-life is the time required for half of the radioactive nuclei in a sample to decay. Knowing the half-life allows one to predict how the number of radioactive atoms decreases over time and to relate the measured radioactivity (for example, the number of decays occurring over a given period) back to the original number of atoms present.

Neutron Activation Analysis

Neutron activation analysis is a technique that involves bombarding a sample with neutrons so that nuclei absorb a neutron and become radioactive. This method is useful for detecting and quantifying specific isotopes based on the characteristic radiation they emit during decay.

Gamma Spectroscopy and Detection Efficiency

Gamma spectroscopy involves measuring the energy and intensity of gamma rays emitted by radioactive isotopes. With knowledge of the detection efficiency and the energy of the photons, one can use the measured energy to calculate the number of decays that occurred and thereby estimate the quantity of the original radioactive atoms.

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