The method and the results are on the atomic structure lab. Do the analysis yourself first, then check the answers below.
Quick answer: An atom has a tiny nucleus of protons and neutrons, with electrons in shells around it. These answers go with the Chemistry 9-10 lab on atomic structure: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
These model answers use the sample results. Firstly, the weighted mean links the bolt model directly to the formula for relative atomic mass, and then the graph shows how the average changes with the mix.
Level: Chemistry grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: HS-PS1-1, GCSE C1
Question 1 Predict handful 1
Firstly, expected mass = 28 × 4.02 + 12 × 5.98 = 112.56 + 71.76 = 184.32 g. mean = 184.32 ÷ 40 = 4.608 g.Expected mean = 4.61 g, the same as measured.
Question 2 Compare with measurements
Handful 2: 25 × 4.02 + 15 × 5.98 = 100.50 + 89.70 = 190.20 g (measured 190.1).Then handful 3: 31 × 4.02 + 9 × 5.98 = 124.62 + 53.82 = 178.44 g (measured 178.5).
Finally, handful 4: 22 × 4.02 + 18 × 5.98 = 88.44 + 107.64 = 196.08 g (measured 196.0).
So the differences are 0.1, 0.06 and 0.08 g.
Largest difference = 0.1 g, within balance resolution.
Question 3 Plot the graph
Firstly, fractions: 12 ÷ 40 = 0.300; 15 ÷ 40 = 0.375; 9 ÷ 40 = 0.225; 18 ÷ 40 = 0.450.Then points: (0.300, 4.61), (0.375, 4.75), (0.225, 4.46), (0.450, 4.90).
Therefore, the points lie on a straight line rising from about 4.0 g at x = 0 to about 6.0 g at x = 1.
Question 4 Meaning of intercept and gradient
Firstly, gradient = (4.90 − 4.46) ÷ (0.450 − 0.225) = 0.44 ÷ 0.225 = 1.96 g. This equals 5.98 − 4.02, the difference between the two bolt masses.Then intercept ≈ 4.02 g, the mass of one small bolt (no large bolts).
Gradient 1.96 g; intercept 4.02 g.
Question 5 Link to isotopes
(a) Each size of bolt is like an isotope with its own mass.(b) Also, the fraction of each size of bolt in the handful matches the percentage abundance.
(c) Finally, the mean mass per bolt matches the relative atomic mass.
Bolt size = isotope; fraction = abundance; mean mass = Ar.
Question 6 Not a bolt mass
The mean is a weighted average of two masses, 4.02 g and 5.98 g, so it falls between them. No bolt weighs 4.61 g.Chlorine is similar because its Ar of 35.5 is an average, and no chlorine atom has a mass number of 35.5.
The average falls between the two masses and matches nothing single.
Question 7 Balance uncertainty
Firstly, percentage uncertainty in total = 0.1 ÷ 184.4 × 100 = 0.054 %.Then dividing by exactly 40 does not change the percentage, so the mean mass also has 0.054 % uncertainty, about ±0.002 g.
0.054 %, so the mean is 4.61 ± 0.003 g (rounded).
Question 8 Estimate an unknown mixture
Firstly, mean = 192.0 ÷ 40 = 4.80 g. Fraction = (4.80 − 4.02) ÷ 1.96 = 0.78 ÷ 1.96 = 0.398, so about 40 % large bolts.Finally, to improve it, use more handfuls of different sizes and a balance reading to 0.01 g.
About 40 % large bolts.
