Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Because of the 1986 explosion and fire in a reactor at the Chernobyl nuclear power plant in northern Ukraine, part of Ukraine is contaminated with $^{137} Cs$ ,which undergoes beta-minus decay with a half-life of 30.2y . In 1996, the total activity of this contamination over an area of $2.6 \times 10^{5} {km}^{2}$ was estimated to be $1 \times 10^{16} Bq$ . Assume that the $^{137} Cs$ is uniformly spread over that area and that the beta-decay electrons travel either directly upward or directly downward. How many beta-decay electrons would you intercept were you to lie on the ground in that area for (a) in 1996 and (b) today? (You need to estimate your cross-sectional area that intercepts those electrons.)

The number of beta-decay electrons that would be intercepted by me if I were to lie on the ground in that area for 1h in 1996 is $7 \times 10^{7}$ .
The number of beta-decay electrons that would be intercepted by me if I were to lie on the ground in that area for 1h in today is $3.85 \times 10^{7}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Write the given data

$R = 1 \times 10^{16} Bq$ Half-life of $^{137} Cs$ , $T_{1 / 2} = 30.2 y$
Total activity of the contamination, $R = 1 \times 10^{16} Bq$
Area of contamination, $A = 2.6 \times 10^{5} {km}^{2}$
Time of contamination, t = 1 h

Step 2: Determine the concept of decay

The abundance of decay defines as the decay acting in the portion. That is the fraction of the portion at which the decay is happening respectively to the whole ground area. Similarly, using this concept, we can get the rate of contamination passing through my body. Now, using this data, and the time of decay, we can get further contamination after the given time within my body.

The activity of the undecayed nuclei with the given time is as follows:

$R = R_{0} e^{- (\frac{I n 2}{T_{1 / 2}}) t}$ …… (i)

Step 3: a) Determine the number of electrons intercepted by me in 1996

Assuming a “target” area of one square meter, we establish a ratio:

$\frac{rate throughme}{total rate upward} = \frac{1 m^{2}}{(2.6 \times 10^{5} {km}^{2}) (1000 m^{2} / {km}^{2})} = 3.8 \times 10^{- 12}$

The SI unit Becquerel is equivalent to a disintegration per second. With half the beta-decay electrons moving upward, the total rate through me can be given as:

$rate through me = \frac{1}{2} (1 \times 10^{16} \frac{1}{s}) (3.8 \times 10^{- 12}) = 1.9 \times 10^{4} \frac{1}{s} \approx 7 \times 10^{7} \frac{1}{h}$

Hence, in one hour $7 \times 10^{7}$ electrons would be intercepted by me.

Step 4: b) Determine the number of electrons intercepted by me in today

For the current year 2022, thus the time of decay becomes

t = (2022 - 1996)

= 26y

Now, using the given data in equation (i), determine the rate of decay in the present given time as follows:

$R = (7 \times 10^{7} h^{- 1}) e^{- (\frac{In 2}{30.2}) 26 y} = (7 \times 10^{7} h^{- 1}) e^{- 0.59675} = 3.85 \times 10^{7} h^{- 1}$

Hence, the number of electrons intercepted by me in one hour is $3.85 \times 10^{7}$ .

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Write the given data

Step 2: Determine the concept of decay

Step 3: a) Determine the number of electrons intercepted by me in 1996

Step 4: b) Determine the number of electrons intercepted by me in today

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Fundamentals Of Physics

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Step 1: Write the given data

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Step 4: b) Determine the number of electrons intercepted by me in today

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