The accompanying graph illustrates the decay of 88 42 Mo, which decays via positron emission. (b) What is the rate constant for the decay? [Section 21.4]

Welcome back everyone. We're told that the decay of selenium 72 by electron capture is illustrated in the following plot. And based on this plot, estimate the half life of the decay. So based on our plot below, we can see that we begin with a mass of our selenium 72 of about one g here. Because on our white access it's measured in units of g. So we can say we begin at one graham of Selenium 72. And we recognize from the plot that with the decay of electron capture or by electron capture of our selenium 72 We're going to lose 50% of this initial mass of our selenium 72. And so half of our initial mass of one g is going to be about we would say .5 here. So we'll say after Electron capture we have about .5g of our selenium 72 left or that remains. And so going to this point point five here 50.5 g. We're gonna carry this across to our line and we're going to see that this land us just a bit past eight days. So we'll say that this is about and let's actually draw the line in. So 0.5 g going to our graph will say that this hits at just about 8.3 and our X axis is measured in days. So we would say that Our half life of our selenium 72 Is about 8. days. And this would be our final answer. 8.5 days that it takes for our electron capture to leave us with .5g of our selenium 72. I hope everything I reviewed was clear. If you have any questions, leave them down below and I'll see everyone in the next practice video.

Ch.21 - Nuclear Chemistry

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Brown 14th Edition

Ch.21 - Nuclear Chemistry

Problem 6b

Chapter 21, Problem 6b

The accompanying graph illustrates the decay of ⁸⁸₄₂Mo, which decays via positron emission. (b) What is the rate constant for the decay? [Section 21.4]

Verified step by step guidance

Identify the type of decay process: The problem states that ⁸⁸₄₂Mo decays via positron emission. This is a type of radioactive decay where a proton is converted into a neutron, releasing a positron and a neutrino.

Understand the relationship between half-life and the rate constant: The rate constant (k) for a first-order decay process can be determined using the relationship between the half-life (t_1/2) and the rate constant, given by the formula: t_1/2 = \( \frac{0.693}{k} \).

Determine the half-life from the graph: Analyze the graph provided to find the time it takes for the amount of ⁸⁸₄₂Mo to decrease to half of its initial value. This time is the half-life (t_1/2).

Use the half-life to calculate the rate constant: Once the half-life is known, rearrange the formula to solve for the rate constant: k = \( \frac{0.693}{t_1/2} \).

Substitute the half-life value into the equation: Insert the half-life value obtained from the graph into the equation to find the rate constant k.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This can occur through various modes, including alpha decay, beta decay, and positron emission. In the case of the isotope 88Mo, positron emission involves the conversion of a proton into a neutron, resulting in the emission of a positron and a neutrino.

Rate Constant

The rate constant (k) is a proportionality factor in the equation that describes the rate of a chemical reaction or decay process. For radioactive decay, it is related to the half-life of the substance and indicates how quickly the substance will decay. The relationship is given by the equation k = ln(2) / t1/2, where t1/2 is the half-life.

Exponential Decay

Exponential decay describes the process by which the quantity of a radioactive substance decreases over time at a rate proportional to its current value. This can be mathematically represented by the equation N(t) = N0 e^(-kt), where N(t) is the quantity at time t, N0 is the initial quantity, and k is the rate constant. Understanding this concept is crucial for calculating the rate constant from decay data.