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Physics - Nuclear Physics

Grade 10IGCSE

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

🔑Concepts

The atom consists of a nucleus containing protons and neutrons (nucleons), surrounded by electrons. The notation for a nuclide is ZAX^A_Z X, where AA is the nucleon (mass) number and ZZ is the proton (atomic) number.

Isotopes are atoms of the same element with the same number of protons (ZZ) but different numbers of neutrons (different AA).

Radioactive decay is a random process in which unstable nuclei emit radiation to become more stable. The three main types are alpha (α\alpha), beta (β\beta), and gamma (γ\gamma).

Alpha (α\alpha) particles are Helium nuclei (24He^4_2\text{He}). They have high ionizing power, low penetration (stopped by paper), and are deflected by electric/magnetic fields.

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

Gamma (γ\gamma) rays are high-frequency electromagnetic waves. They have low ionizing power but very high penetration (reduced by thick lead or concrete).

Half-life (T1/2T_{1/2}) is the time taken for half the nuclei of a radioactive isotope in a sample to decay, or the time taken for the activity (measured in Becquerels, BqBq) to halve.

Nuclear fission is the splitting of a large nucleus into two smaller daughter nuclei, releasing energy. Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, occurring in stars at very high temperatures.

Background radiation is the low-level radiation present from natural sources (radon gas, cosmic rays, rocks) and artificial sources (medical X-rays, fallout).

📐Formulae

Nucleon Number (A)=Protons (Z)+Neutrons (N)\text{Nucleon Number (A)} = \text{Protons (Z)} + \text{Neutrons (N)}

ZAXZ2A4Y+24α(Alpha Decay)^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2\alpha \quad (\text{Alpha Decay})

ZAXZ+1AY+10β(Beta Decay)^A_Z X \rightarrow ^A_{Z+1} Y + ^0_{-1}\beta \quad (\text{Beta Decay})

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

N=N0×(12)nwhere n=tT1/2N = N_0 \times \left(\frac{1}{2}\right)^n \quad \text{where } n = \frac{t}{T_{1/2}}

💡Examples

Problem 1:

A sample of 88226Ra^ {226}_{88}\text{Ra} undergoes alpha decay. Determine the proton number and nucleon number of the resulting Radon (RnRn) nucleus.

Solution:

The resulting nucleus is 86222Rn^{222}_{86}\text{Rn}.

Explanation:

In α\alpha decay, the nucleus emits a 24He^4_2\text{He} particle. Therefore, the nucleon number AA decreases by 44 (2264=222226 - 4 = 222) and the proton number ZZ decreases by 22 (882=8688 - 2 = 86).

Problem 2:

A radioactive source has an initial activity of 800 Bq800\text{ Bq}. If its half-life is 10 minutes10\text{ minutes}, calculate its activity after 30 minutes30\text{ minutes}.

Solution:

100 Bq100\text{ Bq}

Explanation:

First, find the number of half-lives: n=30 min10 min=3n = \frac{30\text{ min}}{10\text{ min}} = 3. After 1 half-life: 800/2=400 Bq800 / 2 = 400\text{ Bq}. After 2 half-lives: 400/2=200 Bq400 / 2 = 200\text{ Bq}. After 3 half-lives: 200/2=100 Bq200 / 2 = 100\text{ Bq}.

Problem 3:

Complete the beta decay equation for Carbon-14: 614CZAN+10β^{14}_{6}\text{C} \rightarrow ^A_Z \text{N} + ^0_{-1}\beta. Find AA and ZZ.

Solution:

A=14,Z=7A = 14, Z = 7

Explanation:

In β\beta decay, a neutron changes into a proton and an electron. The nucleon number AA remains unchanged (1414), while the proton number ZZ increases by 11 (6+1=76 + 1 = 7).