IB · E · structured
Nuclear and quantum physics · Question 8
Nuclear and quantum physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 12
- Topics
- 2
- Answer
- Complete
The nuclide ²²⁶₈₈Ra decays by alpha emission with a half-life of 1600 years. A sealed sample initially contains 3.0 × 10²¹ radium-226 nuclei.
- (a)
State State the nucleon number and the proton number of the nuclide produced by this decay.
2 marks - (b)
Determine Determine the initial activity of the sample, in becquerel.
4 marks - (c)
Explain Explain what is meant by saying that radioactive decay is both random and spontaneous.
2 marks - (d)
Explain Explain why the emission spectrum of a gas consists of discrete lines rather than a continuous range of wavelengths, and outline what this shows about the atom.
4 marks
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(a)
State State the nucleon number and the proton number of the nuclide produced by this decay.
Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.
- 1
Alpha emission reduces the nucleon number by four, giving 222.
- 2
Alpha emission reduces the proton number by two, giving 86.
(b)
Determine Determine the initial activity of the sample, in becquerel.
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
t½ = 1600 years = 1600 × 3.15 × 10⁷ = 5.04 × 10¹⁰ s
- 2
λ = ln 2 / t½ = 0.693 / 5.04 × 10¹⁰ = 1.37 × 10⁻¹¹ s⁻¹
- 3
A = λN = 1.37 × 10⁻¹¹ × 3.0 × 10²¹
- 4
A = 4.1 × 10¹⁰ Bq
(c)
Explain Explain what is meant by saying that radioactive decay is both random and spontaneous.
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
random: it cannot be predicted which nucleus will decay next, or when a particular nucleus will decay — only the probability per unit time is known
- 2
spontaneous: the decay is unaffected by external conditions such as temperature, pressure or chemical state
(d)
Explain Explain why the emission spectrum of a gas consists of discrete lines rather than a continuous range of wavelengths, and outline what this shows about the atom.
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
an atom emits a photon when an electron moves from a higher to a lower energy level
- 2
the photon energy equals the difference between the two levels, and its wavelength follows from E = hc/λ
- 3
only certain transitions are possible, so only certain photon energies — and hence only certain wavelengths — are emitted
- 4
this shows that the energy of an electron in an atom is quantised, taking only discrete values rather than any value in a range
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