Question 31.18: Figure 31.13 shows the decay of a radioactive isotope of cae...

Cambridge International AS and A Level Physics Coursebook

Figure 31.13 shows the decay of a radioactive isotope of caesium, $^{134} _{55}Cs$ . Use the graph to determine the half-life of this nuclide in years, and hence find the decay constant in $year^{−1}$ .

31.13

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Question: 31.20

The isotope 7^16 N decays with a half-life of 7.4 s. a Calculate the decay constant for this nuclide. b A sample of 7^16 N initially contains 5000 nuclei. Determine how many will remain after a time of: i 14.8 s ii 20.0 s ...

Verified Answer:

a Decay constant

λ = \frac{0.693}{7.4} = 0....

Question: 31.2

Copy and complete this equation for the β^− decay of a nucleus of argon: 18^41 Ar → K + ? ...

Verified Answer:

^{41} _{18}Ar → ^{41} _{19}K + ^{0}_{-1...

Question: 31.1

Study the decay equations given in Worked examples 1 and 2, and write balanced equations for the following: a A nucleus of radon-220 ( 86^220 Rn) decays by α emission to form an isotope of polonium, Po. b A nucleus of a sodium isotope ( 11^25 Na) decays by β^− emission to form an isotope of ...

Verified Answer:

a

^{220} _{86}Rn → ^{216} _{84}Po + ^{...

Question: 31.21

A sample contains an isotope of half-life t1/2 . a Show that the fraction f of nuclei in the sample which remain undecayed after a time t is given by the equation: f = (1/2)^n when n = t/t1/2 b Calculate the fraction f after each of the following times: i t1/2 ii 2t1/2 iii 2.5t1/2 iv 8.3t1/2 ...

Verified Answer:

a We need to find an expression for the decay cons...

Question: 31.19

The decay constant of a particular isotope is known to be 3.0 × 10^−4 s^−1. Determine how long it will take for the activity of a sample of this substance to decrease to one-eighth of its initial value. ...

Verified Answer:

Time taken for activity to decrease to

\fr...

Question: 31.17

The value of λ for protactinium-234 is 9.63 × 10^−3 s^−1. Table 31.5 shows the number of undecayed nuclei, N, in a sample. Copy and complete Table 31.5. Draw a graph of N against t, and use it to find the half-life t1/2 of protactinium-234. ...

Verified Answer:

t / s 0 20 40 60 80 100 120 140 N 400 330 272 22...

Question: 31.16

A sample of an isotope for which λ = 0.10 s^−1 contains 5.0 × 10^9 undecayed nuclei at the start of an experiment. Determine: a the number of undecayed nuclei after 50 s b its activity after 50 s. ...

Verified Answer:

a

N = N_{0} e^{–λt} = 5.0 × 10^{9} × e^{(–...

Question: 31.15

The isotope nitrogen-13 has a half-life of 10 min. A sample initially contains 8.0 × 10^10 undecayed nuclei. a Write down an equation to show how the number undecayed, N, depends on time, t. b Determine how many nuclei will remain after 10 min, and after 20 min . c Determine how many nuclei will ...

Verified Answer:

N = N_{0}  e^{–λt}

b After 10 minut...

Question: 31.WE.8

A sample initially contains 1000 undecayed nuclei of an isotope whose decay constant λ = 0.10 min^−1. Draw a graph to show how the sample will decay over a period of 10 minutes. ...

Verified Answer:

Step 1 We have

N_{0} = 1000

and [la...

Question: 31.WE.7

Suppose we start an experiment with 1.0 × 10^15 undecayed nuclei of an isotope for which λ is equal to 0.02 s^−1. Determine the number of undecayed nuclei after 20s. ...

Verified Answer:

Step 1 In this case, we have

N_{0} = 1.0 × ...