Radiation and Radioactivity ：練習問題

When a radioactive nucleus undergoes \(\beta^{-}\) decay, what happens to its atomic number (\(Z\)) and mass number (\(A\))?

A radioactive source has an activity of \(3.0 \times 10^5\text{ Bq}\). If the decay constant of the isotope is \(1.5 \times 10^{-8}\text{ s}^{-1}\), how many undecayed nuclei are present in the sample?

A specific radioactive isotope used in medical imaging has a physical half-life of \(6.0\text{ hours}\). When administered to a patient, the body also eliminates the isotope biologically with a biological half-life of \(3.0\text{ hours}\). If the initial activity of the isotope in the patient is \(400\text{ MBq}\), what is the activity remaining in the patient after \(4.0\text{ hours}\)?

Which of the following correctly lists alpha (α), beta (β), and gamma (γ) radiations in order of decreasing ionizing power?

A student uses a Geiger-Müller counter to measure the count rate of a radioactive source. At time \(t = 0\), the recorded count rate is \(420 \text{ cpm}\). After two half-lives of the source have passed, the recorded count rate is \(120 \text{ cpm}\). Assuming the background count rate remains constant throughout the experiment, what is the background count rate?

A radioactive source contains a mixture of two isotopes, A and B. At time \(t = 0\), the activity of isotope A is 8 times the activity of isotope B. Given that the half-life of A is \(2 \text{ hours}\) and the activity of isotope A becomes equal to that of isotope B after \(12 \text{ hours}\), calculate the half-life of isotope B in hours.

A radioactive sample contains two different radioisotopes, A and B. Initially, the activity of A is twice that of B. The half-life of A is \(3.0 \text{ hours}\) and the half-life of B is \(9.0 \text{ hours}\). Determine the time, in hours, when the activities of both isotopes will be equal.

A specific radioisotope has a decay constant of \(0.0231 \text{ h}^{-1}\). A researcher observes that the activity of a sample of this isotope is initially \(800 \text{ Bq}\). If a second sample of a different isotope with a half-life of \(15 \text{ hours}\) initially has an activity of \(200 \text{ Bq}\), calculate the time \(t\) in hours when both samples will have the exact same activity.

A student uses a Geiger-Muller (GM) counter to investigate the radioactive decay of a sample. The student first measures the background radiation for 10 minutes and obtains a total of 180 counts.

(a) Calculate the average background count rate in counts per minute (cpm).
(b) The radioactive source is placed in front of the GM counter. The initial count rate recorded is 458 cpm. Determine the corrected initial count rate.
(c) After 12 hours, the corrected count rate of the sample is found to be 55 cpm. Calculate the half-life of the radioactive isotope in hours.
(d) State one safety precaution the student should take when handling the radioactive source in the laboratory.

A student uses a Geiger-Muller (GM) counter to investigate the radioactivity of a sample. Before placing the sample, the student records the background radiation and obtains 480 counts over a period of 15 minutes. The sample is then placed near the detector, and the initial count rate is measured to be 652 counts per minute (cpm). After a period of 9.0 hours, the count rate is measured again and found to be 109 cpm.

(a) Calculate the average background count rate in cpm.
(b) Determine the corrected initial count rate and the corrected count rate after 9.0 hours.
(c) Calculate the half-life of the radioactive isotope in the sample.