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Question 21N.2.HL.TZ0.4

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Date November 2021 Marks available [Maximum mark: 19] Reference code 21N.2.HL.TZ0.4
Level HL Paper 2 Time zone TZ0
Command term Calculate, Draw, Estimate, Explain, Identify, Show that, State, Suggest Question number 4 Adapted from N/A
4.
[Maximum mark: 19]
21N.2.HL.TZ0.4
(a.i)

State what is meant by the binding energy of a nucleus.

[1]

Markscheme

the energy needed to «completely» separate the nucleons of a nucleus

OR

the energy released when a nucleus is assembled from its constituent nucleons ✓

 

Accept reference to protons and neutrons.

(a.ii)

Draw, on the axes, a graph to show the variation with nucleon number A of the binding energy per nucleon, BEA. Numbers are not required on the vertical axis.

[2]

Markscheme

curve rising to a maximum between 50 and 100 ✓

curve continued and decreasing ✓

 

Ignore starting point.

Ignore maximum at alpha particle.

(a.iii)

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

[1]

Markscheme

At a point on the peak of their graph ✓

(a.iv)

Some unstable nuclei have many more neutrons than protons. Suggest the likely decay for these nuclei.

[1]

Markscheme

beta minus «decay» ✓

Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).

The following data are available for binding energies per nucleon:

plutonium          7.568 MeV

uranium             7.600 MeV

alpha particle     7.074 MeV

(b.i)

Show that the energy released in this decay is about 6 MeV.

[3]

Markscheme

correct mass numbers for uranium (234) and alpha (4) ✓

234×7.600+4×7.074-238×7.568 «MeV» ✓

energy released 5.51 «MeV» ✓

 

Ignore any negative sign.

(b.ii)

The plutonium nucleus is at rest when it decays.

Calculate the ratio kinetic energy of alpha particlekinetic energy of uranium.

[2]

Markscheme

«KEαKEU=»p22mαp22mU  OR  mUmα ✓

«2344=» 58.5 ✓

 

Award [2] marks for a bald correct answer.

Accept 1172 for MP2.

The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10−10 s−1.

(c.i)

Estimate the power, in kW, that is available from the plutonium at launch.

[3]

Markscheme

number of nuclei present =33×103238×6.02×1023«=8.347×1025» ✓

initial activity is λN0=2.5×10-10×8.347×1025«=2.08×1016 Bq» ✓

power is 2.08×1016×5.51×106×1.6×10-19≈18 «kW» ✓

 

Allow a final answer of 20 kW if 6 MeV used.

Allow ECF from MP1 and MP2.

(c.ii)

The spacecraft will take 7.2 years (2.3 × 108 s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.

[2]

Markscheme

available power after time t is P0e−λt ✓

18e−2.50×10−10×2.3×108=17.0 «kW» ✓

 

MP1 may be implicit.

Allow ECF from (c)(i).

Allow 17.4 kW from unrounded power from (c)(i).

Allow 18.8 kW from 6 MeV.

Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is monochromatic. The spacecraft is moving away from the Sun.

(d.i)

 State and explain what happens to the kinetic energy of an emitted photoelectron.

[2]

Markscheme

stays the same ✓

as energy depends on the frequency of light ✓

 

Allow reference to wavelength for MP2.

Award MP2 only to answers stating that KE decreases due to Doppler effect.

(d.ii)

 State and explain what happens to the rate at which charge leaves the metallic surface.

[2]

Markscheme

decreases ✓

as number of photons incident decreases ✓

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