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30 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1

2

a b

Write down Einstein’s famous equation relating mass and energy. Determine the change in energy equialent to a change in mass! i of 1." g ii equal to that of an electron $%.1 × 1"&'1 (g ( g).

a

b

1# .-

.

Determine the mass of each of the following particles in terms of u! i an /particle of mass .0 × 1"&# (g (g ii a carbon1' atom of mass #.1 × 1"&# (g (g. Determine the mass of each of the following particles in (ilograms! i a proton of mass 1."1 u ii a uranium#'0 nucleus of mass #'2.%% u.

3

3tate three qu quantities consered in all nuclear reactions.

4

a b

E4plain why e4ternal energy is required to 5split’ a nucleus. Define the binding energy of of a nucleus.

c

+he binding energy of the nuclide

6

[#] [#]

*n nuclear physics, it is common practice to quote the mass of a nuclear particle in terms of the unified atomic mass unit, u. +he unified atomic mass unit u is defined as onetwelfth of the mass of an atom of the carbon isotope

5

[1]

1. 76

[1] [1] [1] [1] ['] [1] [1]

is 1#7 8e9. -alculate the binding energy

per nucleon.

[#]

Define the half-life of of a radioactie isotope. +he halflife of a particular isotope is #" minutes. : sample initially contains N " nuclei of this isotope. Determine the number of nuclei of the isotope left in t he sample after! i #" minutes ii 1." hour.

[1]

[1] [#]

+he actiity of an /source is 02" ;q. +he (inetic energy of each /particle is 7. < 1" &12 =. +he isotope in the source has a ery long halflife. a -alculate the number of /particles emitted by the source in! i 1 second ii 1 hour. b Determine the total energy released by the source in a time of 1 second. c 3tate the rate at which energy is emitted from this /source.

[1] [1] ['] [1]

a b

:3 and : >eel ?hysics

6riginal material @ -ambridge Aniersity ?ress #"1"

1

30 Worksheet (A2)

7

+he binding energy per nucleon against nucleon number graph for some common nuclides is shown below.

a

*dentify the most stable nuclide. E4plain your answer.

b

Ase the graph to estimate the binding energy for the nucleus of

c

Ase the gr graph to estimate the energy released in the following fusion reaction. # 1

d

8

[#] 1# .-

B

#

.

[#] [2]

2

+ 1 B → # Be

+he fusion reaction shown in c is one of the many that occur in the interior of stars. 3tate the conditions necessary to initiate such reactions in stars.

[#]

Ase the data gien below to determine the binding bi nding energy and the binding energy per nucleon of the nuclide

#'0 %# A

.

mass of proton = 1."" u mass of neutron = 1.""% 1.""% u

:3 and : >eel ?hysics

[] mass mass of ura urani nium um#' #'0 0 nucl nucleu euss = #'2.%%# u

6riginal material @ -ambridge Aniersity ?ress #"1"

2

30 Worksheet (A2)

9

a b

Describe the process of induced nuclear fission. +he diagram shows the fission of uranium#'0 in accordance with the nuclear equation! #'0 1 %0 1'% %# A + " n → '7 3r + 02 Ce +

i ii

[1]

1

#" n

-opy the diagram, adding labels to identify the neutrons, the strontium nuclide and the 4enon nuclide. E4plain why energy is released in the reaction aboe.

[1] [#]

iii Ase the following data to determine the energy released in a single fission reaction

inoling

#'0 A %#

and

1 "n

.

[0]

mass of

#'0 A = %#

mass of

%0 '7 3r =

mass of

1 "n

mass of

1'% 02

'.%"# × 1"� (g

1.0 × 1"&# (g

=

1.00 × 1"� (g

Ce

#.'" × 1"� (g

=

10 6ne of the neutroninduced fission reactions of uranium#'0 may be represented b y the following nuclear equations. #'0 %# A #'. %#

A

1 "n

→

12. 0

→

#'. %# A

>a

7 '0 ;r

' "1 n

+he binding energies per nucleon for these nuclides are! #'. %#

A, .0% 8e9

12. 0

>a, 7.21 8e9

7 '0 ;r,

-alculate the energy released in 8e9 when the 11 +he halflife of the radon isotope

##" 7.

7.0% 8e9.

#'. %# A

nu nucleus undergoes fission.

[']

Fn is 0 s.

a

Determine the decay constant in s &1.

b

-alculate the actiity of a sample containing ." × 1"1" nuclei of

['] ##" 7.

Fn .

[']

12 +he actiity of a radioactie source containing 7." × 1"12 undecayed nuclei is 0." × 1"% ;q. a Determine the decay constant in s &1. b -alculate the halflife of the nucleus. c Bow many undecayed nuclei will be left after 2" hoursG 13 a b

Define the decay constant of of a nucleus. +he thorium isotope

## %"

[1]

+h has a halflife of 17 days.

: particular radioactie source contains 2." × 1"1# nuclei of the isotope i

['] ['] [']

Determine the decay constant for the thorium isotope

## %"

## %"

+h .

+h in s&1.

[']

ii What is the initial actiity of the sourceG iii -alculate the actiity of the source after ' days.

['] [#]

14 : sample of roc( is (nown to contain 1." Hg of the radioactie radium isotope

##. 77 Fa

.

+he halflife of this particular isotope is 1"" years. +he molar mass of radium## is ## g. ##. 77 Fa

a

Determine the number of nuclei of the isotope

b

-alculate the actiity from decay of the radium## in the sample.

:3 and : >eel ?hysics

in in the roc( sample.

6riginal material @ -ambridge Aniersity ?ress #"1"

[#] [']

3

30 Worksheet (A2)

15 *n a process referred to as 5annihilation’, a particle interacts with its antiparticle and the entire mass of the combined particles is transformed into energy in the form of photons. +he following equation represents the interaction of a proton $p) and its antiparticle, the antiproton $ p ). 1 1 1 p + −1 p →

I+I

+he antiproton has the same mass as a proton J the onl y difference is that it has a negatie charge. Determine the waelength λ of of each of the two identical photons emitted in the reaction aboe. $8ass of a proton = 1. × 1"&# (g (g.)

[0]

16 Does fusion or fission produce more energy per (ilogram of fuelG :nswer this question by considering the fusion reaction in 7 c and the fission reaction in 9 b. $+he mol molaar ma masses ses of of hy hydrogen# an and ur uranium ium#'0 ar are # g an and #' #'0 g, g, re respe spectiely. ly.)

[]

17 3ome astronomers beliee that our solar system was formed 0." < 1" % years ago. :ssuming that all uranium#'7 nuclei were formed before this time, what fraction of the original uranium#'7 nuclei remain in the s olar system todayG +he isotope of uranium #'7 %# A

has a halflife of 2.0 × 1"% y. y.

[2]

+otal!

:3 and : >eel ?hysics

1""

3core!

6riginal material @ -ambridge Aniersity ?ress #"1"

K

4

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2

a b

Write down Einstein’s famous equation relating mass and energy. Determine the change in energy equialent to a change in mass! i of 1." g ii equal to that of an electron $%.1 × 1"&'1 (g ( g).

a

b

1# .-

.

Determine the mass of each of the following particles in terms of u! i an /particle of mass .0 × 1"&# (g (g ii a carbon1' atom of mass #.1 × 1"&# (g (g. Determine the mass of each of the following particles in (ilograms! i a proton of mass 1."1 u ii a uranium#'0 nucleus of mass #'2.%% u.

3

3tate three qu quantities consered in all nuclear reactions.

4

a b

E4plain why e4ternal energy is required to 5split’ a nucleus. Define the binding energy of of a nucleus.

c

+he binding energy of the nuclide

6

[#] [#]

*n nuclear physics, it is common practice to quote the mass of a nuclear particle in terms of the unified atomic mass unit, u. +he unified atomic mass unit u is defined as onetwelfth of the mass of an atom of the carbon isotope

5

[1]

1. 76

[1] [1] [1] [1] ['] [1] [1]

is 1#7 8e9. -alculate the binding energy

per nucleon.

[#]

Define the half-life of of a radioactie isotope. +he halflife of a particular isotope is #" minutes. : sample initially contains N " nuclei of this isotope. Determine the number of nuclei of the isotope left in t he sample after! i #" minutes ii 1." hour.

[1]

[1] [#]

+he actiity of an /source is 02" ;q. +he (inetic energy of each /particle is 7. < 1" &12 =. +he isotope in the source has a ery long halflife. a -alculate the number of /particles emitted by the source in! i 1 second ii 1 hour. b Determine the total energy released by the source in a time of 1 second. c 3tate the rate at which energy is emitted from this /source.

[1] [1] ['] [1]

a b

:3 and : >eel ?hysics

6riginal material @ -ambridge Aniersity ?ress #"1"

1

30 Worksheet (A2)

7

+he binding energy per nucleon against nucleon number graph for some common nuclides is shown below.

a

*dentify the most stable nuclide. E4plain your answer.

b

Ase the graph to estimate the binding energy for the nucleus of

c

Ase the gr graph to estimate the energy released in the following fusion reaction. # 1

d

8

[#] 1# .-

B

#

.

[#] [2]

2

+ 1 B → # Be

+he fusion reaction shown in c is one of the many that occur in the interior of stars. 3tate the conditions necessary to initiate such reactions in stars.

[#]

Ase the data gien below to determine the binding bi nding energy and the binding energy per nucleon of the nuclide

#'0 %# A

.

mass of proton = 1."" u mass of neutron = 1.""% 1.""% u

:3 and : >eel ?hysics

[] mass mass of ura urani nium um#' #'0 0 nucl nucleu euss = #'2.%%# u

6riginal material @ -ambridge Aniersity ?ress #"1"

2

30 Worksheet (A2)

9

a b

Describe the process of induced nuclear fission. +he diagram shows the fission of uranium#'0 in accordance with the nuclear equation! #'0 1 %0 1'% %# A + " n → '7 3r + 02 Ce +

i ii

[1]

1

#" n

-opy the diagram, adding labels to identify the neutrons, the strontium nuclide and the 4enon nuclide. E4plain why energy is released in the reaction aboe.

[1] [#]

iii Ase the following data to determine the energy released in a single fission reaction

inoling

#'0 A %#

and

1 "n

.

[0]

mass of

#'0 A = %#

mass of

%0 '7 3r =

mass of

1 "n

mass of

1'% 02

'.%"# × 1"� (g

1.0 × 1"&# (g

=

1.00 × 1"� (g

Ce

#.'" × 1"� (g

=

10 6ne of the neutroninduced fission reactions of uranium#'0 may be represented b y the following nuclear equations. #'0 %# A #'. %#

A

1 "n

→

12. 0

→

#'. %# A

>a

7 '0 ;r

' "1 n

+he binding energies per nucleon for these nuclides are! #'. %#

A, .0% 8e9

12. 0

>a, 7.21 8e9

7 '0 ;r,

-alculate the energy released in 8e9 when the 11 +he halflife of the radon isotope

##" 7.

7.0% 8e9.

#'. %# A

nu nucleus undergoes fission.

[']

Fn is 0 s.

a

Determine the decay constant in s &1.

b

-alculate the actiity of a sample containing ." × 1"1" nuclei of

['] ##" 7.

Fn .

[']

12 +he actiity of a radioactie source containing 7." × 1"12 undecayed nuclei is 0." × 1"% ;q. a Determine the decay constant in s &1. b -alculate the halflife of the nucleus. c Bow many undecayed nuclei will be left after 2" hoursG 13 a b

Define the decay constant of of a nucleus. +he thorium isotope

## %"

[1]

+h has a halflife of 17 days.

: particular radioactie source contains 2." × 1"1# nuclei of the isotope i

['] ['] [']

Determine the decay constant for the thorium isotope

## %"

## %"

+h .

+h in s&1.

[']

ii What is the initial actiity of the sourceG iii -alculate the actiity of the source after ' days.

['] [#]

14 : sample of roc( is (nown to contain 1." Hg of the radioactie radium isotope

##. 77 Fa

.

+he halflife of this particular isotope is 1"" years. +he molar mass of radium## is ## g. ##. 77 Fa

a

Determine the number of nuclei of the isotope

b

-alculate the actiity from decay of the radium## in the sample.

:3 and : >eel ?hysics

in in the roc( sample.

6riginal material @ -ambridge Aniersity ?ress #"1"

[#] [']

3

30 Worksheet (A2)

15 *n a process referred to as 5annihilation’, a particle interacts with its antiparticle and the entire mass of the combined particles is transformed into energy in the form of photons. +he following equation represents the interaction of a proton $p) and its antiparticle, the antiproton $ p ). 1 1 1 p + −1 p →

I+I

+he antiproton has the same mass as a proton J the onl y difference is that it has a negatie charge. Determine the waelength λ of of each of the two identical photons emitted in the reaction aboe. $8ass of a proton = 1. × 1"&# (g (g.)

[0]

16 Does fusion or fission produce more energy per (ilogram of fuelG :nswer this question by considering the fusion reaction in 7 c and the fission reaction in 9 b. $+he mol molaar ma masses ses of of hy hydrogen# an and ur uranium ium#'0 ar are # g an and #' #'0 g, g, re respe spectiely. ly.)

[]

17 3ome astronomers beliee that our solar system was formed 0." < 1" % years ago. :ssuming that all uranium#'7 nuclei were formed before this time, what fraction of the original uranium#'7 nuclei remain in the s olar system todayG +he isotope of uranium #'7 %# A

has a halflife of 2.0 × 1"% y. y.

[2]

+otal!

:3 and : >eel ?hysics

1""

3core!

6riginal material @ -ambridge Aniersity ?ress #"1"

K

4

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