OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(i) the equations e A A t 0 = m - and e N N t 0 = m - , where A is the…
Full specification wording
Radioactivity: (i) the equations e A A t 0 = m - and e N N t 0 = m - , where A is the activity and N is the number of undecayed nuclei
These equations describe exponential decay of activity and of undecayed nuclei.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 8 of 11
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
These equations describe exponential decay of activity and of undecayed nuclei. In the intended form, A = A₀e^(−λt) and N = N₀e^(−λt), where A is activity at time t, A₀ is initial activity, N is the number of undecayed nuclei at time t, N₀ is the initial number, λ is the decay constant and t is elapsed time. Activity is the rate of decay, measured in becquerels, where 1 Bq = 1 decay per second. The decay constant λ has unit s⁻¹. Because both A and N follow the same exponential form, the ratio A/N is constant and equals λ. Half-life is related to the decay constant by T½ = ln2/λ. The equations apply to large numbers of nuclei and describe random decay statistically.
What earns the marks
- The equation A = A₀e^(−λt) relates activity at time t to initial activity, decay constant and elapsed time.
- The equation N = N₀e^(−λt) relates the number of undecayed nuclei at time t to the initial number.
- λ is the decay constant with unit s⁻¹, and t is the elapsed time.
- Activity is the rate of decay measured in becquerels, where 1 Bq = 1 decay per second.
- The ratio A/N equals the decay constant λ because both quantities decay with the same exponential form.
- Half-life is related to the decay constant by T½ = ln2/λ.
Common mistakes and how to put them right
Using a positive exponent instead of a negative one, which would describe growth rather than decay.
Put it right: The exponent is −λt.
Confusing activity with the number of undecayed nuclei.
Put it right: Activity is the rate of decay in Bq, while N is a count of nuclei.
Treating λ as having unit s rather than s⁻¹.
Put it right: λ has unit s⁻¹ because λt must be dimensionless.
Assuming the equations predict exactly when an individual nucleus decays.
Put it right: Decay is random and the equations describe statistical behaviour of large numbers.
Exam tips
- Check that λt is dimensionless before substituting values into the exponential.
- Remember that A and N share the same exponential factor, so their ratio stays constant at λ.
- Convert half-life to the decay constant using λ = ln2/T½ before applying the decay equations.
Try the lesson
The start of the Radioactivity: (i) the equations e A A t 0 = m - and e N N t 0 = m - , where A is the activity and N is the number of undecayed nuclei lesson, made from checked teaching notes for this specification point.
Listen
These equations describe exponential decay of activity and of undecayed nuclei. In the intended form, A = A₀e^(−λt) and N = N₀e^(−λt), where A is activity at time t, A₀ is initial activity, N is the number of undecayed nuclei at time t, N₀ is the initial number, λ is the decay constant and t is elapsed time. Activity is the rate of decay, measured in becquerels, where 1 Bq = 1 decay per second. The decay constant λ has unit s⁻¹. Because both A and N follow the same exponential form, the ratio A/N is constant and equals λ. Half-life is related to the decay constant by T½ = ln2/λ. The equations apply to large numbers of nuclei and describe random decay statistically. A strong answer earns marks for these points. The equation A = A₀e^(−λt) relates activity at time t to initial activity, decay constant and elapsed time. The equation N = N₀e^(−λt) relates the number of undecayed nuclei at time t to the initial number. λ is the decay constant with unit s⁻¹, and t is the elapsed time. Activity is the rate of decay measured in becquerels, where 1 Bq = 1 decay per second. A common slip: Using a positive exponent instead of a negative one, which would describe growth rather than decay. Instead, the exponent is −λt. Exam tip: Check that λt is dimensionless before substituting values into the exponential.
See it
Key words
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Exponential decay of activity
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Exponential decay of undecayed nuclei
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Decay constant and its unit
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Relationship between half-life and decay constant
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See every definition
- Exponential decay of activity
- The equation A = A₀e^(−λt) relates activity at time t to initial activity, decay constant and elapsed time.
- Exponential decay of undecayed nuclei
- The equation N = N₀e^(−λt) relates the number of undecayed nuclei at time t to the initial number.
- Decay constant and its unit
- λ is the decay constant with unit s⁻¹, and t is the elapsed time.
- Relationship between half-life and decay constant
- Half-life is related to the decay constant by T½ = ln2/λ.
Label the diagram
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1Box 1
2Box 2
3Box 3
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