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Question 22M.2.HL.TZ1.9b.ii

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Date May 2022 Marks available [Maximum mark: 3] Reference code 22M.2.HL.TZ1.9b.ii
Level HL Paper 2 Time zone TZ1
Command term Estimate Question number b.ii Adapted from N/A
b.ii.
[Maximum mark: 3]
22M.2.HL.TZ1.9b.ii

Potassium-40 K1940 decays by two processes.

The first process is that of beta-minus (β−) decay to form a calcium (Ca) nuclide.

Potassium-40 decays by a second process to argon-40. This decay accounts for 11 % of the total decay of the potassium-40.

Rocks can be dated by measuring the quantity of argon-40 gas trapped in them. One rock sample contains 340 µmol of potassium-40 and 12 µmol of argon-40.

(b.ii)

The half-life of potassium-40 is 1.3 × 109 years. Estimate the age of the rock sample.

[3]

Markscheme

ALTERNATIVE 1

λ=ln2t12 used to give 𝜆 = 5.3 x 10-10 per year ✓


340=449e-5.3×10-10×t

OR

ln340449=-5.3×10-10×t  ✓


t = 5.2 x 108 «years» ✓

 

ALTERNATIVE 2

p=340449=0.76 «remaining» ✓

n=lnp0.693=ln0.760.693=0.40 ✓

t = 0.40 x 1.3 x 109 = 5.2 x 108 «years» ✓

 

ALTERNATIVE 3

p=340449=0.76 «remaining» ✓

0.76=12t1.3×109 ✓

t = 0.40 x 1.3 x 109 = 5.2 x 108 «years» ✓

 

Allow 5.3 x 108 years for final answer.

Allow ECF for MP3 for an incorrect number of half-lives.

Examiners report

This was a more challenging question for candidates. Many were able to calculate the decay constant and recognized that the ratio of initial and final quantities of the potassium-40 was important. A very common error was mixing the two common half-life equations up and using the wrong values in the exponent (using half life instead of the decay constant, or using the decay constant instead of the half life). Examiners were generous with ECF for candidates who clearly showed an incorrect number of half-lives multiplied by the time for one half-life.

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