A Level · A2 · structured
A Level extension · Question 11
A Level extension · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 14
- Topics
- 2
- Answer
- Complete
Electrons are accelerated from rest through a potential difference of 250 V. Separately, a nucleus of ⁵⁶₂₆Fe has a nuclear mass of 55.9206 u. The mass of a proton is 1.00728 u, the mass of a neutron is 1.00867 u, and 1 u is equivalent to 931.5 MeV.
- (a)
Calculate Calculate the de Broglie wavelength of the accelerated electrons.
4 marks - (b)
Explain Explain how the diffraction of a beam of such electrons by a thin crystal provides evidence for the wave nature of matter.
3 marks - (c)
Determine Determine the binding energy per nucleon of ⁵⁶₂₆Fe, in MeV.
4 marks - (d)
Explain Iron-56 lies near the peak of the binding energy per nucleon curve. Explain why energy is released both when light nuclei fuse and when heavy nuclei undergo fission.
3 marks
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(a)
Calculate Calculate the de Broglie wavelength of the accelerated electrons.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
kinetic energy = eV = 1.60 × 10⁻¹⁹ × 250 = 4.0 × 10⁻¹⁷ J
- 2
p = √(2mE_k) = √(2 × 9.11 × 10⁻³¹ × 4.0 × 10⁻¹⁷)
- 3
p = 8.5 × 10⁻²⁴ kg m s⁻¹
- 4
λ = h/p = 6.63 × 10⁻³⁴ / 8.5 × 10⁻²⁴ = 7.8 × 10⁻¹¹ m
(b)
Explain Explain how the diffraction of a beam of such electrons by a thin crystal provides evidence for the wave nature of matter.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
the beam produces a pattern of rings or maxima and minima rather than a single spot
- 2
diffraction and interference are effects that only waves show
- 3
the spacing of the pattern agrees with the de Broglie wavelength calculated from the electrons' momentum, so the wavelength is a property of the particles themselves
(c)
Determine Determine the binding energy per nucleon of ⁵⁶₂₆Fe, in MeV.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
total mass of separate nucleons = 26 × 1.00728 + 30 × 1.00867 = 56.4494 u
- 2
mass defect Δm = 56.4494 − 55.9206 = 0.5288 u
- 3
binding energy = 0.5288 × 931.5 = 492.6 MeV
- 4
per nucleon = 492.6 / 56 = 8.8 MeV
(d)
Explain Iron-56 lies near the peak of the binding energy per nucleon curve. Explain why energy is released both when light nuclei fuse and when heavy nuclei undergo fission.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
energy is released whenever the products have a greater binding energy per nucleon than the reactants, because the nucleons end up more tightly bound and the surplus mass is released as energy
- 2
light nuclei lie to the left of the peak, so fusing them moves the nucleons up the curve towards iron
- 3
heavy nuclei lie to the right of the peak, so splitting them also moves the nucleons up the curve towards iron
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