Nuclear Physics Test. 5

For light elements, the stable ratio is ~1:1. For heavier elements, more neutrons are needed to counteract the increasing electrostatic repulsion between protons, so the n/p ratio increases.

By conservation of momentum, the KE of the alpha particle is KE_α = Q × (A-4)/A, where A is the mass number of the parent. KE_α = 4.27 MeV × (234/238) ≈ 4.20 MeV.

Spontaneous decay means it occurs randomly for any given nucleus and cannot be sped up or slowed down by external factors like temperature, pressure, or chemical environment.

The decay constant λ is related to the half-life T₁/₂ by the formula λ = 0.693 / T₁/₂. So, λ = 0.693 / 1600 yr ≈ 4.33 x 10⁻⁴ yr⁻¹.

The energy released (Q-value) is the mass difference (Δm) multiplied by 931.5 MeV. Δm = 4.0028 - 4.0010 = 0.0018 amu. So, E = 0.0018 × 931.5 ≈ 1.677 MeV.

Solid-state detectors produce a signal whose size is proportional to the energy deposited by the radiation, allowing for precise energy measurement (spectroscopy). G-M counters cannot do this.

By international agreement, the standard for the atomic mass unit is based on the Carbon-12 atom, which is defined as having a mass of exactly 12 amu.

The primary fusion process in the Sun is the proton-proton chain, in which four hydrogen nuclei (protons) are ultimately converted into one helium nucleus, releasing energy.

This energy must be at least the sum of the rest mass energies of the electron (0.511 MeV) and the positron (0.511 MeV), which totals 1.022 MeV.

Leptons are a class of fundamental particles that do not experience the strong nuclear force. The electron, muon, tau, and their corresponding neutrinos are all leptons.

Isomers are nuclei with the same number of protons and neutrons but are in different excited, metastable energy states. They decay via gamma emission or internal conversion.

The CNO (Carbon-Nitrogen-Oxygen) cycle is a catalytic fusion process that is the dominant source of energy in stars more massive than our Sun.

The binding energy per nucleon is the total binding energy divided by the mass number (A). For Lithium-7, A=7. So, 39.2 MeV / 7 nucleons = 5.6 MeV/nucleon.

The Sievert (Sv) is the unit of equivalent dose, which accounts for both the amount of energy deposited (in Grays) and the biological effectiveness of the type of radiation.

Activity is defined as the number of nuclear decays per unit time. One Becquerel (Bq) is equal to one decay per second.

The activity reduces from 1000 Bq to 125 Bq. 1000 → 500 → 250 → 125. This is 3 steps, meaning 3 half-lives have passed. Total time = 3 × 28 years = 84 years.

The mass number changes by 4, so there is 1 alpha decay (¹⁰Po -> ²⁰⁶X). This would make Z=82. The daughter is Pb (Z=82), but the parent Po is Z=84. To reduce Z by 2, one alpha decay is needed. No, wait.  ¹⁰Po (Z=84) -> ¹ alpha + ²⁰⁶X (Z=82). The daughter IS ²⁰⁶Pb (Z=82). Hmm, let me re-evaluate common decay chains. Let's assume a decay chain starting higher up. U-238 to Pb-206 is 8 alpha, 6 beta. That's too complex. Let's assume the question is a net change. A change of 4 in mass number = 1 alpha. A change of -2 in atomic number (84->82) is consistent with 1 alpha decay. But some decay chains involve beta decays in between. The question as stated is simply 1 alpha. Let me find a better example or stick to the direct interpretation. Let's stick to the simplest path. Oh, the prompt has a typo. Let's re-examine U-238 to Pb-206. A changes by 32. 32/4 = 8 alpha decays. This reduces Z by 16 (92->76). To get to Z=82, we need 6 beta decays (76+6=82). Let me use a clearer question. Let's re-use the Th->Ra question logic here. Let me fix the question to be clearer. Ok, I'll provide an explanation for the most direct path. Change in A = 210-206=4. This requires 4/4 = 1 alpha decay. This alpha decay changes Z by -2 (84 -> 82). The final Z is 82, so no beta decays are needed for charge balance. The correct answer must be '1 alpha, 0 beta'. I will adjust the options.

The mass number (A) is the total number of nucleons (protons + neutrons), and the atomic number (Z) is the number of protons. Therefore, the number of neutrons is the difference: A - Z.

A charged particle ionizes the vapor as it passes through. These ions then act as nucleation sites for tiny droplets of liquid to condense, forming a visible trail.

The photon is the quantum of the electromagnetic field and mediates the electromagnetic force between charged particles. Gluons mediate the strong force.