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Nuclear Physics - Radioactivity (Alpha, beta and gamma radiation)

Grade 11A LevelPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Radioactivity is the random and spontaneous emission of radiation from an unstable nucleus as it attempts to reach a more stable state.

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Alpha (α\alpha) particles are helium nuclei (24He^{4}_{2}\text{He}) consisting of two protons and two neutrons. They have a +2e+2e charge, high ionizing power, and low penetrating power (stopped by a sheet of paper or a few cm of air).

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Beta (β\beta) particles are high-speed electrons (−10e^{0}_{-1}\text{e}) emitted when a neutron turns into a proton in the nucleus. They have a −1e-1e charge, moderate ionizing power, and moderate penetrating power (stopped by a few mm of aluminium).

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Gamma (γ\gamma) rays are high-energy electromagnetic waves (00γ^{0}_{0}\gamma). they have no mass or charge, low ionizing power, and very high penetrating power (requiring thick lead or several meters of concrete to be absorbed).

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Deflection in Electric/Magnetic Fields: Alpha particles are deflected towards negative plates, Beta particles (being lighter) are deflected more strongly towards positive plates, and Gamma rays remain undeflected.

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Background radiation is the low-level radiation present from natural sources (cosmic rays, radon gas, rocks) and artificial sources (medical X-rays, nuclear fallout). Corrected count rate is calculated as: Total Count−Background CountTotal\ Count - Background\ Count.

📐Formulae

Alpha Decay: ZAX→Z−2A−4Y+24α\text{Alpha Decay: } ^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\alpha

Beta Decay: ZAX→Z+1AY+−10e\text{Beta Decay: } ^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^{0}_{-1}\text{e}

Gamma Emission: ZAX∗→ZAX+00γ\text{Gamma Emission: } ^{A}_{Z}X^* \rightarrow ^{A}_{Z}X + ^{0}_{0}\gamma

Corrected Count Rate=Measured Count Rate−Background Count Rate\text{Corrected Count Rate} = \text{Measured Count Rate} - \text{Background Count Rate}

💡Examples

Problem 1:

A nucleus of Uranium-238 (92238U^{238}_{92}\text{U}) undergoes alpha decay to form Thorium (ThTh). Determine the mass number (AA) and atomic number (ZZ) of the Thorium nucleus.

Solution:

Mass number A=238−4=234A = 238 - 4 = 234; Atomic number Z=92−2=90Z = 92 - 2 = 90. The resulting nucleus is 90234Th^{234}_{90}\text{Th}.

Explanation:

In alpha decay, the parent nucleus loses 2 protons and 2 neutrons. Therefore, the mass number decreases by 4 and the atomic number decreases by 2.

Problem 2:

Carbon-14 (614C^{14}_{6}\text{C}) decays by emitting a beta particle to form Nitrogen (NN). Write the balanced nuclear equation.

Solution:

614C→714N+−10e^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}

Explanation:

In beta decay, a neutron changes into a proton and an electron. The atomic number increases by 1 (from 6 to 7), while the mass number remains the same (14).

Problem 3:

A Geiger-Müller counter records a total count of 120120 counts per minute (cpm). If the background radiation in the room is 1515 cpm, calculate the actual activity of the radioactive source.

Solution:

120 cpm−15 cpm=105 cpm120\text{ cpm} - 15\text{ cpm} = 105\text{ cpm}

Explanation:

To find the true activity of a source, you must subtract the background radiation from the total detected count rate.