The initial activity a sample of 1 mole of radon-220 is 8 . 02 × 10 21 s - 1 . Calculate: (b) the half-life of the isotope.

Given, Activity A = 8 . 02 × 10 21 s - 1 Using the formula of activity decay constant is given by A = λ N λ = A N = 8 . 02 × 10 21 6 . 02 × 10 23 = 1 . 33 × 10 - 2 The half-life of the radon-220 is given by λ t 1 / 2 = 0 . 693 t 1 / 2 = 0 . 693 λ = 0 . 693 1 . 33 × 10 - 2 = 52 . 0 s

The initial activity a sample of 1 mole of radon-220 is 8 . 02 × 10 21 s - 1 . Calculate: (b) the half-life of the isotope.

Given, Activity A = 8 . 02 × 10 21 s - 1 Using the formula of activity decay constant is given by A = λ N λ = A N = 8 . 02 × 10 21 6 . 02 × 10 23 = 1 . 33 × 10 - 2 The half-life of the radon-220 is given by λ t 1 / 2 = 0 . 693 t 1 / 2 = 0 . 693 λ = 0 . 693 1 . 33 × 10 - 2 = 52 . 0 s

The graph of count rate against time for a sample containing indium-116 is shown. (a) Use the graph to determine the half-life of the isotope.

From the graph, 2 × t 1 / 2 = 28 s t 1 / 2 = 28 2 = 14 s

The proportions of different isotopes in rocks can be used to date the rocks. The half-life of uranium-238 is 4 . 9 × 10 9 years. A sample has 99 . 2 % of the proportion of this isotope compared with newly formed rock. (a) Calculate the decay constant in y - 1 for this isotope of uranium.

Given, t 1 / 2 = 4 . 9 × 10 9 y e a r s Using the formula, λ = 0 . 693 t 1 / 2 = 0 . 693 4 . 9 × 10 9 = 1 . 4 × 10 - 10 y - 1

The proportions of different isotopes in rocks can be used to date the rocks. The half-life of uranium-238 is 4 . 9 × 10 9 years. A sample has 99 . 2 % of the proportion of this isotope compared with newly formed rock. (b) Calculate the age of the rock in years.

Given, Half-life t 1 / 2 = 4 . 9 × 10 9 y e a r s The age of the rock is given by ln N N ∘ = - λ t ln ( 0 . 992 ) = - 1 . 4 × 10 - 10 × t t = 5 . 7 × 10 7 y r

The table shows the received count rate when a sample of the isotope vanadium- 52 decays. Time / min 0 1 2 3 4 5 6 7 8 Count rate / s - 1 187 159 134 110 85 70 60 56 40 (a) (ii) Comment on the scattering of the points.

When a sample of the isotope vanadium- 52 decays, a curve is obtained between its count rate and time.There is a random element of radioactive decay, which becomes more apparent at lower levels of activity.

The table shows the received count rate when a sample of the isotope vanadium- 52 decays. Time / min 0 1 2 3 4 5 6 7 8 Count rate / s - 1 187 159 134 110 85 70 60 56 40 (b) From the graph, determine the half-life of the isotope.

The graph obtained is given below, Half-life of the isotope is given by using the graph t 1 / 2 ~ 3 . 8 m i n u t e s

The table shows the received count rate when a sample of the isotope vanadium- 52 decays. Time / min 0 1 2 3 4 5 6 7 8 Count rate / s - 1 187 159 134 110 85 70 60 56 40 (c) Describe the changes to the graph that you would expect if you were given a larger sample of the isotope.

When a sample of the isotope vanadium- 52 decays and if we are given a larger sample of the isotope then all count rates would be greater but the time for the rate to halve would remain the same.

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AS and A Level

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The initial activity a sample of 1 mole of radon-220 is $8.02 \times 10^{21} s^{- 1}$ .

Calculate:

(b) the half-life of the isotope.

Important Questions on Nuclear Physics

HARD

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 10

The graph of count rate against time for a sample containing indium-116 is shown.

Question Image

(a) Use the graph to determine the half-life of the isotope.

HARD

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 10

The graph of count rate against time for a sample containing indium-116 is shown.

Question Image

(b) Calculate the decay constant.

HARD

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 11

The proportions of different isotopes in rocks can be used to date the rocks. The half-life of uranium-238 is $4.9 \times 10^{9}$ years. A sample has $99.2 %$ of the proportion of this isotope compared with newly formed rock.

(a) Calculate the decay constant in $y^{- 1}$ for this isotope of uranium.

HARD

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 11

(b) Calculate the age of the rock in years.

MEDIUM

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 12

The table shows the received count rate when a sample of the isotope vanadium- $52$ decays.

$Time / min$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$Count rate / s^{- 1}$	$187$	$159$	$134$	$110$	$85$	$70$	$60$	$56$	$40$

(a) (i) Sketch a graph of the count rate against the time.

MEDIUM

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 12

The table shows the received count rate when a sample of the isotope vanadium- $52$ decays.

$Time / min$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$Count rate / s^{- 1}$	$187$	$159$	$134$	$110$	$85$	$70$	$60$	$56$	$40$

(a) (ii) Comment on the scattering of the points.

HARD

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 12

The table shows the received count rate when a sample of the isotope vanadium- $52$ decays.

$Time / min$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$Count rate / s^{- 1}$	$187$	$159$	$134$	$110$	$85$	$70$	$60$	$56$	$40$

(b) From the graph, determine the half-life of the isotope.

HARD

AS and A Level

IMPORTANT

Physics for Cambridge International AS & A Level Coursebook 3rd Edition Digital Access>Chapter 29 - Nuclear Physics>EXAM-STYLE QUESTIONS>Q 12

The table shows the received count rate when a sample of the isotope vanadium- $52$ decays.

$Time / min$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$Count rate / s^{- 1}$	$187$	$159$	$134$	$110$	$85$	$70$	$60$	$56$	$40$

The initial activity a sample of 1 mole of radon-220 is 8.02×1021 s-1. Calculate: (b) the half-life of the isotope.

Important Questions on Nuclear Physics

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The initial activity a sample of 1 mole of radon-220 is $8.02 \times 10^{21} s^{- 1}$ .

Calculate:

(b) the half-life of the isotope.