Radioactivity：練習問題

A student uses a Geiger-Muller tube to measure the count rate from a radioactive source. With paper placed between the source and the tube, the count rate drops slightly. When 5 mm of aluminum is added, the count rate drops significantly to the background level. What type of radiation is being emitted by the source?

A gamma radiation source produces a corrected count rate of \(400 \text{ min}^{-1}\) at a distance of \(0.20 \text{ m}\) from a detector. The background count rate is constant at \(20 \text{ min}^{-1}\). What will be the total (uncorrected) count rate measured by the detector when it is moved to a distance of \(0.50 \text{ m}\) from the source?

In the process of ̴̵̶̷̸̢̡̢̧̨̛̖̗̘̙̜̝̞̟̠̣̤̥̦̩̪̫̬̭̮̯̰̱̲̳̹̺̻̼͇͈͉͍͎́̀̂̃̄̅̆̇̈̉̊̋̌̍̎̏̐̑̒̓̔̽̾̿̀́͂̓̈́͆͊͋͌̕̚ͅ͏͓͔͕͖͙͚͐͑͒͗͛ͣͤͥͦͧͨͩͪͫͬͭͮͯ͘͜͟͢͝͞͠͡⁻ beta-plus (β⁺) decay, a proton in a nucleus is converted into a neutron. Which of the following pairs of particles are also emitted from the nucleus during this process?

The decay of a free neutron is represented by the equation:
\( n \rightarrow p + e^- + \bar{\nu}_e \)
Which of the following statements correctly describes the conservation laws in this decay?

Technetium-99m is widely used as a radioactive tracer in medical imaging. Which of the following properties makes it particularly suitable for this application?

A radioactive nucleus \(X\) decays into a nucleus \(Y\) after emitting one alpha particle and two beta-minus particles. Compare the atomic number of \(X\) and \(Y\).

A detector is placed at a fixed distance from a radioactive source used to monitor the thickness of paper in a mill. If the detected count rate increases, what change has occurred in the thickness of the paper?

A point source of gamma radiation produces an intensity of \(800 \text{ counts per minute}\) at a distance of \(1.5 \text{ m}\). Calculate the count rate at a distance of \(4.5 \text{ m}\).

A student uses a Geiger-Müller (GM) tube and a counter to investigate the radiation from a gamma source.

(a) The average background count rate is measured as \(35\) counts per minute (cpm). With the gamma source placed \(0.40\) m from the detector, the counter reads \(435\) cpm. Calculate the corrected count rate at this distance.

(b) Using the inverse-square law for gamma radiation, predict the expected total count rate (including background) when the source is moved to a distance of \(1.20\) m from the detector.

(c) Compare the ionizing power and penetrating power of alpha radiation with that of gamma radiation.

(d) Explain why the existence of the neutrino was hypothesized to account for the energy spectrum of electrons emitted in beta-minus decay.