*TYPE B*
1(a)
Young's modulus
Bulk modulus
Shear modulus
1(b)
i. Elasticity – the property of a material that enables it to return to its original shape and size after the deforming force is removed.
ii. Plasticity – the property of a material that causes it to retain a permanent deformation after the deforming force is removed (it does not return to its original shape).
iii. Ductility – the ability of a material to be drawn or stretched into thin wires without breaking.
iv. Malleability – the ability of a material to be hammered or rolled into thin sheets without breaking.
1(c) x = 4t² − 16t + 12
v = dx/dt = 8t − 16
a = dv/dt = 8
i. Instantaneous velocity at t = 5s:
v = 8(5) − 16 = 24 m/s
ii. Instantaneous acceleration:
a = 8 m/s²
iii. stationary (v = 0):
8t − 16 = 0 → t = 2 s
1(a)
Young's modulus
Bulk modulus
Shear modulus
1(b)
i. Elasticity – the property of a material that enables it to return to its original shape and size after the deforming force is removed.
ii. Plasticity – the property of a material that causes it to retain a permanent deformation after the deforming force is removed (it does not return to its original shape).
iii. Ductility – the ability of a material to be drawn or stretched into thin wires without breaking.
iv. Malleability – the ability of a material to be hammered or rolled into thin sheets without breaking.
1(c) x = 4t² − 16t + 12
v = dx/dt = 8t − 16
a = dv/dt = 8
i. Instantaneous velocity at t = 5s:
v = 8(5) − 16 = 24 m/s
ii. Instantaneous acceleration:
a = 8 m/s²
iii. stationary (v = 0):
8t − 16 = 0 → t = 2 s
8(a)i. Heisenberg's Uncertainty Principle states that
It is impossible to simultaneously measure both the exact position and exact momentum of a particle with unlimited precision.
Δx · Δp ≥ h/4π
8(a)ii.
-Medical diagnosis (imaging bones, detecting fractures/tumours)
-Airport/security baggage screening
-Industrial radiography (detecting cracks/flaws in metals and welds)
-Crystallography (studying the structure of crystals)
8(b) Wavelength, λ = 1 Å = 1 × 10⁻¹⁰ m
i. Energy of photon in eV:
E = hc/λ = (6.626×10⁻³⁴ × 3×10⁸) / (1×10⁻¹⁰)
E = 1.988 × 10⁻¹⁵ J
E = 1.988×10⁻¹⁵ / 1.6×10⁻¹⁹
E ≈ 12,424 eV ≈ 12.4 keV
ii. Momentum of photon:
p = h/λ = 6.626×10⁻³⁴ / 1×10⁻¹⁰
p ≈ 6.63 × 10⁻²⁴ kg·m/s
8(c)i.
Binding energy is the energy required to completely separate a nucleus into its individual constituent nucleons
or equivalently, the energy released when free nucleons combine to form the nucleus.
It is impossible to simultaneously measure both the exact position and exact momentum of a particle with unlimited precision.
Δx · Δp ≥ h/4π
8(a)ii.
-Medical diagnosis (imaging bones, detecting fractures/tumours)
-Airport/security baggage screening
-Industrial radiography (detecting cracks/flaws in metals and welds)
-Crystallography (studying the structure of crystals)
8(b) Wavelength, λ = 1 Å = 1 × 10⁻¹⁰ m
i. Energy of photon in eV:
E = hc/λ = (6.626×10⁻³⁴ × 3×10⁸) / (1×10⁻¹⁰)
E = 1.988 × 10⁻¹⁵ J
E = 1.988×10⁻¹⁵ / 1.6×10⁻¹⁹
E ≈ 12,424 eV ≈ 12.4 keV
ii. Momentum of photon:
p = h/λ = 6.626×10⁻³⁴ / 1×10⁻¹⁰
p ≈ 6.63 × 10⁻²⁴ kg·m/s
8(c)i.
Binding energy is the energy required to completely separate a nucleus into its individual constituent nucleons
or equivalently, the energy released when free nucleons combine to form the nucleus.
❤4
2(a)
K₂Cr₂O₇:
2(+1) + 2(x) + 7(−2) = 0
2 + 2x − 14 = 0
2x = 12
x = +6 (Cr)
Na₂S₂O₃:
2(+1) + 2(x) + 3(−2) = 0
2 + 2x − 6 = 0
2x = 4
x = +2 (S)
2(b)
(i) Cl⁻ : 1s² 2s² 2p⁶ 3s² 3p⁶
(ii) Fe³⁺ : 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵
K₂Cr₂O₇:
2(+1) + 2(x) + 7(−2) = 0
2 + 2x − 14 = 0
2x = 12
x = +6 (Cr)
Na₂S₂O₃:
2(+1) + 2(x) + 3(−2) = 0
2 + 2x − 6 = 0
2x = 4
x = +2 (S)
2(b)
(i) Cl⁻ : 1s² 2s² 2p⁶ 3s² 3p⁶
(ii) Fe³⁺ : 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵