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A pure sample of nuclide X containing N nuclei has an activity A - AQA - A-Level Physics - Question 29 - 2017 - Paper 2
Question 29
A pure sample of nuclide X containing N nuclei has an activity A. The half-life of X is 6000 years. A pure sample of nuclide Y containing 3N nuclei has an activity ... show full transcript
Worked Solution & Example Answer:A pure sample of nuclide X containing N nuclei has an activity A - AQA - A-Level Physics - Question 29 - 2017 - Paper 2
Step 1
What is the relationship between activity and number of nuclei?
Answer
The activity of a radioactive sample is directly proportional to the number of undecayed nuclei present in the sample. This means that if the number of nuclei is increased, the activity will also increase proportionally.
Mathematically, this relationship can be expressed as: A = rac{ ext{Decay constant} imes N}{ ext{Half-life}}
Step 2
Determine the half-life of nuclide Y.
Answer
Given that nuclide Y contains 3N nuclei and has an activity of 6A, we can set up the relationship using the formula for activity.
For nuclide Y:
- Activity (Y) = 6A
- Number of nuclei (Y) = 3N
Since the activity is proportional to the number of nuclei,
defining the decay constants:
- For nuclide X, we have: A = rac{ ext{Decay constant}_X imes N}{6000}
- For nuclide Y: 6A = rac{ ext{Decay constant}_Y imes 3N}{T_Y}
Where T_Y is the half-life of nuclide Y.
Equating the ratios, we can find T_Y as follows: rac{6A}{A} = rac{3N}{N} imes rac{6000}{T_Y} This simplifies to: 6 = 3 imes rac{6000}{T_Y} Solving for T_Y, we get: T_Y = rac{3 imes 6000}{6} = 3000 ext{ years}.