12.2 Nuclear Physics

Question 1

Marks: 1

A radioactive source X consists of 10.4 × 10¹¹ atoms of a nuclide of half-life 5 days. A second source Y consists of 5.2 × 10¹⁰ atoms of another nuclide of half-life 6 days.

After how many days will the number of radioactive atoms in X be equal to Y?

$\frac{30 \ln (2)}{\ln (20)}$
$\frac{\ln (20)}{30 \ln (2)}$
$\frac{30 \ln (20)}{\ln (2)}$
$\frac{\ln (2)}{30 \ln (20)}$

Key Concepts

Measuring Half-Life

Question 2

Marks: 1

Two radioactive elements X and Y have half–lives T_X and T_Y respectively. Initially samples of S, N_X contains three times as many atoms of Y, N_Y .

After a certain time t, which of the expressions for $\frac{n u m b e r o f d e c a y e d a t o m s o f X}{n u m b e r o f d e c a y e d a t o m s o f Y}$ is correct?

$\frac{3 (N_{Y} - N_{Y} {(\frac{1}{2})}^{\frac{t}{T_{X}}})}{N_{Y} - N_{Y} {(\frac{1}{2})}^{\frac{t}{T_{Y}}}}$
$\frac{N_{X} {(\frac{1}{2})}^{\frac{t}{T_{X}}} - N_{X}}{N_{Y} {(\frac{1}{2})}^{\frac{t}{T_{Y}}} - N_{Y}}$
$\frac{N_{X} {(\frac{1}{2})}^{\frac{t}{T_{X}}}}{N_{Y} {(\frac{1}{2})}^{\frac{t}{T_{Y}}}}$
$\frac{{3 N}_{Y} {(\frac{1}{2})}^{\frac{t}{T_{X}}}}{N_{Y} {(\frac{1}{2})}^{\frac{t}{T_{Y}}}}$

Key Concepts

Measuring Half-Life

Question 3

Marks: 1

The initial activity of a radioactive source is 160 counts per second. After a time T, its activity becomes 5 counts per second.

If the half–life of the source is 18 hours, what is T?

$\frac{\ln (32)}{18 \ln (2)}$ hours
$\frac{18 \ln (32)}{\ln (2)}$ hours
$\frac{\ln (2)}{18 \ln (32)}$ hours
$\frac{18 \ln (2)}{\ln (32)}$ hours

Key Concepts

Measuring Half-Life
Problems Involving the Radioactive Decay Law

Question 4

Marks: 1

A pure sample of a radioactive nuclide has mass m, half-life T_1/2 and initial activity A₀.

Identify the half-life and initial activity of another sample which is otherwise identical but has mass 3m.

	Half-life	Initial activity
A.	$T_{1 / 2}$	$A_{0}$
B.	$3 T_{1 / 2}$	$\frac{1}{3} A_{0}$
C.	$T_{1 / 2}$	$3 A_{0}$
D.	$3 T_{1 / 2}$	$3 A_{0}$

Key Concepts

Problems Involving the Radioactive Decay Law
Measuring Half-Life

Question 5

Marks: 1

Alpha particles with various energy E are directed at a nuclei with atomic number Z. Small deviations from the predictions of the Rutherford scattering model are observed.

Which value of E and Z is most likely to result in the greatest deviations from the Rutherford scattering model?

	E / MeV	Z
A.	39.0	350
B.	2.4	190
C.	39.0	190
D.	2.5	350

Key Concepts

Deviations from Rutherford Scattering

Question 6

Marks: 1

Two radioactive nuclides, P and Q, have half-lives of 70 s and 175 s respectively. At time t = 0, samples of P and Q contain the same number of nuclei.

What is $\frac{n u m b e r o f n u c l e i o f P d e c a y e d}{n u m b e r o f n u c l e i o f Q d e c a y e d}$ when t = 350 s?

8
$\frac{24}{31}$
$\frac{31}{24}$
$\frac{1}{8}$

Key Concepts

The Law of Radioactive Decay
Problems Involving the Radioactive Decay Law

Question 7

Marks: 1

The diameter of Iridium-192 ( ${}_{77}^{192}I r$ ) nucleus is approximately four times that of the diameter of a nucleus of which other isotope?

${}_{1}^{3}H$
${}_{22}^{48}T i$
${}_{5}^{11}B$
${}_{3}^{7}L i$

Key Concepts

Rutherford Scattering & Nuclear Radius

Question 8

Marks: 1

Two unstable isotopes are initially present in equal numbers. Isotope Y has a half life of 6 minutes and isotope Z has a half life of 3 minutes. Which expression correctly describes the ratio of the activity of Y to Z after 12 minutes?

$\frac{e^{- \frac{l n 2}{2} \times 12}}{e^{- \frac{\ln 2}{2} \times 12}}$
$\frac{3}{6} \times \frac{e^{- \ln 2 \times 12}}{e^{- l n 2 \times 12}}$
$\frac{1}{2} \times \frac{e^{- 4 \ln 2}}{e^{- 3 \ln 2}}$
$\frac{1}{2} \times \frac{e^{- 2 \ln 2}}{e^{- 4 \ln 2}}$

Key Concepts

The Law of Radioactive Decay
Problems Involving the Radioactive Decay Law

Question 9

Marks: 1

The ratio $\frac{r a d i u s o f n u c l e u s o f Y}{r a d i u s o f n u c l e u s o f X}$ is equal to 1.2 where the nucleus of X is ${}_{80}^{125}X$ .

How many nucleons does nucleus Y have?

Key Concepts

Rutherford Scattering & Nuclear Radius

Question 10

Marks: 1

A pure sample of a known element has a very short half-life. What measurement(s), together with the initial activity of the sample, must be made in order to measure the half-life of the element?

The number of moles of the sample.
The activity and the number of moles of the sample after a given period of time.
The number of moles after a given period of time.
The activity after a given period of time.

Key Concepts

The Law of Radioactive Decay
Problems Involving the Radioactive Decay Law

DP IB Physics: HL

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12.2 Nuclear Physics

Question 1

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Question 2

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Question 3

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Question 4

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Question 5

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Question 10

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