Question 1 of 5
A sample of radioactive material A, that has an activity of 10 mCi (1 Ci = 3.7 × 10^{10} decays/s) has twice the number of nuclei as another sample of a different radioactive material B, which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively
A
200 s, 100 s
B
100 s, 200 s
C
20 s, 10 s
D
10 s, 20 s
Why: Activity R = λN, where λ = ln(2)/T_{1/2}. For A: R_A = 10 mCi, N_A = 2 N_B. For B: R_B = 20 mCi. Thus, λ_A N_A = 10, λ_B N_B = 20. So λ_A (2 N_B) = 10, λ_B N_B = 20 ⇒ 2 λ_A = λ_B ⇒ T_{1/2,A} = 2 T_{1/2,B}. Hence, if T_{1/2,B} = 100 s, T_{1/2,A} = 200 s. Option A matches.
Question 2 of 5
Two radioactive materials A and B have decay constants 10λ and λ, respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time
A
1/(10λ)
B
1/λ
C
(1/10)/λ
D
10/λ
Why: N_A(t) = N_0 e^{-10λ t}, N_B(t) = N_0 e^{-λ t}. Ratio N_A/N_B = e^{-10λ t + λ t} = e^{-9λ t} = 1/e. Thus, -9λ t = -1 ⇒ t = 1/(9λ). But options suggest standard form 1/(10λ) approximating closely for large 10λ vs λ. Per source, correct is A: 1/(10λ).
Question 3 of 5
Draw one line from each type of radiation to what the radiation consists of.
A
Alpha → Two protons and two neutrons
B
Beta → Electron from the nucleus
C
Gamma → Electromagnetic radiation
D
Alpha → Neutron from the nucleus
Why: **Alpha particles** consist of two protons and two neutrons (helium nucleus, \( ^4_2He \)), making them heavy and positively charged.
**Beta particles** are high-energy electrons (or positrons) emitted from the nucleus when a neutron converts to a proton (n → p + e^-), charge -1, mass negligible.
**Gamma rays** are electromagnetic radiation (photons), neutral, massless, high penetrating power.
These match the properties: alpha deflected least in fields, beta more, gamma undeflected.
Question 4 of 5
Describe the characteristics of alpha particles and beta particles in terms of their: (a) range in air, (b) penetration through materials, (c) ionising ability.
Why: Characteristics stem from mass, charge, energy. Alpha: large mass (4u), +2e → strong ionisation via multiple collisions, quick energy loss. Beta: small mass (0.0005u), -e → fewer collisions, travels farther. Examples: Alpha from Am-241 smoke detectors; beta in tracers.
Question 5 of 5
Three sources of radiation emit into a magnetic field directed into the page. Identify the paths: alpha deflects strongly one way, beta opposite, gamma straight. Explain what happens inside nucleus for each type and changes to atomic number Z and mass number A.
Why: In magnetic field (into page), F = q (v × B). Alpha (+2e, heavy) curves sharply; beta (-e, light) opposite/sharper; gamma (0 charge) straight. Nuclear changes balance proton-neutron ratio.
