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The radioactive nuclide $^{232}_{90}Th$ decays by one $\alpha$ emission followed by two $\beta^-$ emissions - AQA - A-Level Physics - Question 10 - 2020 - Paper 1

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The radioactive nuclide $^{232}_{90}Th$ decays by one $\alpha$ emission followed by two $\beta^-$ emissions. Which nuclide is formed as a result of these decays? A... show full transcript

Worked Solution & Example Answer:The radioactive nuclide $^{232}_{90}Th$ decays by one $\alpha$ emission followed by two $\beta^-$ emissions - AQA - A-Level Physics - Question 10 - 2020 - Paper 1

Step 1

Decay by one $\alpha$ emission

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Answer

When the nuclide 90232Th^{232}_{90}Th undergoes one α\alpha emission, it emits an α\alpha particle (which consists of 2 protons and 2 neutrons). This results in a decrease of 2 in the atomic number and a decrease of 4 in the mass number: 90232Th→88228Rn+α^{232}_{90}Th \rightarrow ^{228}_{88}Rn + \alpha Thus, the first nuclide formed is 88228Rn^{228}_{88}Rn.

Step 2

Followed by two $\beta^-$ emissions

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Answer

In a β−\beta^- decay, a neutron is converted into a proton, resulting in an increase of 1 in the atomic number while the mass number remains unchanged. Performing this twice on 88228Rn^{228}_{88}Rn gives:

  1. First β−\beta^- emission: 88228Rn→89228Fr+β−^{228}_{88}Rn \rightarrow ^{228}_{89}Fr + \beta^-
  2. Second β−\beta^- emission: 89228Fr→90228Th+β−^{228}_{89}Fr \rightarrow ^{228}_{90}Th + \beta^-

Thus, after two β−\beta^- emissions, the final nuclide formed is 90228Th^{228}_{90}Th.

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