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Date November 2020 Marks available 1 Reference code 20N.2.HL.TZ0.6
Level Higher level Paper Paper 2 Time zone 0 - no time zone
Command term Show that Question number 6 Adapted from N/A

Question

One possible fission reaction of uranium-235 (U-235) is

U92235+n01Xe54140+Sr3894+2n01

Mass of one atom of U-235 =235u
Binding energy per nucleon for U-235 =7.59MeV
Binding energy per nucleon for Xe-140 =8.29MeV
Binding energy per nucleon for Sr-94 =8.59MeV

A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to 180MeV of energy.

A sample of waste produced by the reactor contains 1.0kg of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus (β-) decay into a daughter nuclide X. The reaction for this decay is

Sr3894X+v¯e+e.

 

The graph shows the variation with time of the mass of Sr-94 remaining in the sample.

State what is meant by binding energy of a nucleus.

[1]
a(i).

Outline why quantities such as atomic mass and nuclear binding energy are often expressed in non-SI units.

[1]
a(ii).

Show that the energy released in the reaction is about 180MeV.

[1]
a(iii).

Estimate, in Jkg-1, the specific energy of U-235.

[2]
b(i).

The power station has a useful power output of 1.2GW and an efficiency of 36%. Determine the mass of U-235 that undergoes fission in one day.

[2]
b(ii).

The specific energy of fossil fuel is typically 30MJkg1. Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.

[1]
b(iii).

Write down the proton number of nuclide X.

[1]
c(i).

State the half-life of Sr-94.

[1]
c(ii).

Calculate the mass of Sr-94 remaining in the sample after 10 minutes.

[2]
c(iii).

Markscheme

energy required to «completely» separate the nucleons
OR
energy released when a nucleus is formed from its constituent nucleons


Allow protons
AND neutrons.

a(i).

the values «in SI units» would be very small

a(ii).

140×8.29+94×8.59-235×7.59 OR 184«MeV» ✓

a(iii).

see «energy=»180×106×1.60×10-19 AND «mass=»235×1.66×10-27

7.4×1013«Jkg-1» ✓

b(i).

energy produced in one day=1.2×109×24×36000.36=2.9×1014«J»

mass=2.9×10147.4×1013=3.9«kg»

b(ii).

«specific energy of uranium is much greater than that of coal, hence» more energy can be produced from the same mass of fuel / per kg
OR
less fuel can be used to create the same amount of energy ✓

b(iii).

39


Do not allow X3994 unless the proton number is indicated.

c(i).

75«s»

c(ii).

ALTERNATIVE 1

10min=8t1/2 ✓

mass remaining=1.0×128=3.9×10-3«kg»

 

ALTERNATIVE 2

decay constant=«ln275=»9.24×10-3«s-1»

mass remaining=1.0×e-9.24×10-3×600=3.9×10-3«kg»

c(iii).

Examiners report

Generally, well answered but candidates did miss the mark by discussing the constituents of a nucleus rather than the nucleons, or protons and neutrons. There seemed to be fewer comments than usual about 'the energy required to bind the nucleus together'. 

a(i).

Well answered with some candidates describing the values as too large or small.

a(ii).

Well answered.

a(iii).

This caused problems for some with mass often correctly calculated but energy causing more difficulty with the eV conversion either being inaccurate or omitted. Candidates were allowed error carried forward for the second mark as long as they were dividing an energy by a mass.

b(i).

Most candidates had the right idea, but common problems included forgetting the efficiency or not converting to days.

b(ii).

HL only. This was well answered.

b(iii).

Most candidates answered this correctly.

c(i).

Most candidates answered this correctly.

c(ii).

This was answered well with most candidates (even at HL) going down the number of half-lives route rather than the exponential calculation route.

c(iii).

Syllabus sections

Core » Topic 7: Atomic, nuclear and particle physics » 7.2 – Nuclear reactions
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