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Derive an approximate relationship between the energy of $\alpha$ decay and half-life using the following data. It may be useful to graph the log of $t_{1 / 2}$ against $E_{\alpha}$ to find some straight-line relationship.

Hence, from above graph the relation between them is almost linear.

Physics 103

Chapter 31

Radioactivity and Nuclear Physics

Nuclear Physics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

Lectures

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10:02

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01:33

Show that if a radioactive…

02:38

03:22

Consider the models of exp…

01:51

Half-Life The radioactive …

00:46

01:46

01:27

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Half-Life Find the half-li…

(a) The half-life of thori…

03:35

A radioactive nucleus has …

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04:53

03:03

(a) Write the complete $\a…

02:07

Decay of Radium Find the h…

01:40

04:57

So in this question we have data for the alpha decay in the given questions. So now we can convert the values One year equals to three, multiplied by 1.6. Plant weight into the power seven seconds and one microsecond will be close to 10 to the power minus six second and one day will be equals to 864 double zero seconds. So the half life of the alpha decade will be converted into these values. So this this is the table for the question in which these values has been converted in two seconds. So this data will be equals two, 1.8 Multiplied by 10 to the power minus seven second. Okay -7 seconds. And this is already in the seconds of this is your .7 seconds. And after converting 27 days into second we get 2.3 multiplied by 10 to the power six seconds. Okay. And after converting 61,600 years we will get 5.1 Manipulated by 10 to the power 10 seconds. And after converting this number of years in two seconds we get 4.4 multiplied by 10 to the power 17 seconds. Okay, So these are the values fully. He has. No we can take the log as for the requirement of the draft. So the log values for the Question Log T have four different values Will be equals two. This after taking the value law. So we will get -6.7 And this value after taking log we will get -0.15. And after taking log of 2.3, multiplied by 10 to the power six. We will get 6.4. And after taking log of 5.1 multiplayer beta and to the power 10 we will get 10.7. And after taking a log of 4.48 and to the power 17 we will get 17.6. Okay, so now we can plot a graph between this log T half and E alpha, which is energy of the alpha decay. Okay so taking on the X axis on alpha alpha and on the Y axis taking low we will get a graph between them as this. Okay, so this will be the graph for the question which is nearly state like okay we can see these different data points, this data points, this data point, this data point and this data point and this data point. So we can see that a state line is passing through them. Okay, so this is a nearly state line grab. Hence we can say that from the above grab. The relation between them is almost a linear relation. Okay, thank you.

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