Radioactivity：練習問題

A sample of a radioactive isotope has an initial activity of \(640\text{ Bq}\). After a period of \(24\text{ hours}\), the activity has fallen to \(40\text{ Bq}\).
What is the half-life of this isotope?

In β⁻ decay, it was observed that the emitted electrons possess a continuous range of kinetic energies. This observation led Wolfgang Pauli to hypothesize the existence of the antineutrino.
Why was this hypothesis necessary?

Which of the following statements correctly compares the properties of alpha (α) particles and beta-minus (β⁻) particles?

In an industrial thickness-monitoring system for steel sheets approximately \(10\text{ mm}\) thick, a radioactive source is placed on one side of the sheet and a detector on the other.
Which radiation source would be most effective for this system?

A radioactive source is used in an experiment to verify the inverse-square law for gamma (γ) radiation. The corrected count rate at a distance of \(0.20\text{ m}\) from the source is \(1600\text{ counts s}^{-1}\).
What is the expected corrected count rate at a distance of \(0.80\text{ m}\) from the source?

A technician measures the count rate of a gamma-emitting source at two different distances to determine the background radiation in the laboratory. At a distance of \(0.50\text{ m}\), the measured count rate is \(440\text{ counts min}^{-1}\), and at a distance of \(1.00\text{ m}\), the measured count rate is \(140\text{ counts min}^{-1}\). Calculate the background count rate in \(\text{counts min}^{-1}\).

The following table shows the results of an absorption experiment using three different radioactive sources (X, Y, and Z) and various absorbers.

Source X: Count rate reduces to background levels when a single sheet of paper is placed between the source and the detector.
Source Y: Count rate is significantly reduced only after adding several millimeters of Aluminium.
Source Z: Count rate is only significantly reduced by several centimeters of Lead.

(a) Identify the type of radiation emitted by each source (X, Y, and Z).
(b) Explain which of these radiations would be most suitable for monitoring the thickness of Aluminium foil in a manufacturing plant, and why.

In an experiment to verify the inverse-square law for gamma radiation, a student measures the count rate at various distances from a source. The background count rate is constant at \( 30 \text{ counts per minute (cpm)} \).

At a distance of \( 0.20 \text{ m} \), the measured count rate is \( 1230 \text{ cpm} \).
(a) Show that the corrected count rate follows the inverse-square law if at a distance of \( 0.50 \text{ m} \) the measured count rate is \( 222 \text{ cpm} \).
(b) Predict the measured count rate at a distance of \( 0.80 \text{ m} \).
(c) Explain why it is important to measure the count rate over a long period when the source is at a large distance.