1. Which equation correctly shows beta decay?
(A) 210/82 Pb -> 209/81 Tl + 0/-1 e + y
(B) 210/82 Pb -> 209/83 Bi + 0/-1 e + y
(C) 210/82 Pb -> 210/83 Tl + 0/-1 e + y
(D) 210/82 Pb -> 210/83 Bi + y
(E) 210/82 Pb -> 210/83 Bi + 0/-1 e + y
2. The half-life if radon-222 is 3.8 days. If a sample currently has 3.1 grams of radon-222, how much radon-222 did this sample have 15.2 days ago?
(A) 12.4 grams
(B) 47.1 grams
(C) 49.6 grams
(D) 57.8 grams
(E) 92.7 grams
The two questions that I can't figure out on my Science homework. Please help!
(E) 210/82Pb-> 210/83Bi + 0/-1e +Y
(A) 12.4 grams
(E) 210/82 Pb -> 210/83 Bi + 0/-1 e + y
(C) 49.6 grams
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To solve these questions, we need to understand the concepts of beta decay and half-life.
1. Beta decay is a type of radioactive decay in which an unstable nucleus emits a beta particle (an electron or positron) to become more stable. The correct equation for beta decay is represented by the transformation of the atomic numbers and mass numbers on both sides of the equation.
Let's analyze the options given:
(A) 210/82 Pb -> 209/81 Tl + 0/-1 e + y
(B) 210/82 Pb -> 209/83 Bi + 0/-1 e + y
(C) 210/82 Pb -> 210/83 Tl + 0/-1 e + y
(D) 210/82 Pb -> 210/83 Bi + y
(E) 210/82 Pb -> 210/83 Bi + 0/-1 e + y
Option (B) is the correct equation for beta decay. It correctly shows the transformation of atomic numbers and mass numbers on both sides of the equation, representing the emission of a beta particle.
2. The half-life of a radioactive substance is the time it takes for half of the initial quantity to decay. To determine the amount of a substance at a given time, we can use the equation:
N(t) = N₀ * (1/2)^(t / T₁/₂)
Where:
N(t) is the final amount of the substance at time t
N₀ is the initial amount of the substance
T₁/₂ is the half-life of the substance
t is the time elapsed
To solve the problem, we substitute the given values into the equation:
N(t) = 3.1 grams * (1/2)^(15.2 / 3.8)
N(t) = 3.1 grams * (1/2)^4
N(t) = 3.1 grams * 1/16
N(t) = 0.19375 grams
Therefore, 15.2 days ago, the sample had approximately 0.19375 grams of radon-222.
None of the provided answer choices matches this result, so the correct answer may not be listed.