AQA AS Level Physics Paper 1, November 2020: Question 4

10 marks · Medium difficulty · Short Answer

Calculate the mass, number of nucleons, compare nuclear compositions, specific charge, and determine isotopic percentages for boron isotopes X and Y.

Practise this question

Question

A multipart physics question about boron isotopes X and Y. Part 04.1 asks to calculate the mass of an ion of X given its charge and specific charge. Part 04.2 asks to determine the number of nucleons in a nucleus of X given the mass of a nucleon. Part 04.3 compares the nuclear compositions of X and Y. Part 04.4 compares the specific charges of ions of X and Y. Part 04.5 features Table 1 with data for two ionised samples of pure boron, asking to deduce which sample contains a greater percentage of isotope Y.
Question text

04 A sample of pure boron contains only isotope X and isotope Y.

A nucleus of X has more mass than a nucleus of Y.

04.1 The sample is ionised, producing ions each with a charge of +1.6 × 10−19 C.

The specific charge of an ion of X is 8.7 × 106 C kg–1.

Calculate the mass of an ion of X.

[1 mark]

mass of ion = kg

04.2 Determine the number of nucleons in a nucleus of X.

mass of a nucleon = 1.7 × 10–27 kg

[2 marks]

number of nucleons =

04.3 Compare the nuclear compositions of X and Y.

[2 marks]

04.4 Ions of Y have the same charge as ions of X.

State and explain how the specific charge of an ion of X compares with that of an

ion of Y.

*13* [2 marks]

04.5 Table 1 contains data about two completely ionised samples of pure boron.

Each sample contains only isotopes X and Y.

Table 1

Sample Number of ions Mass of Charge on

number in sample sample / kg each ion / C

13.50 × 1016 6.31 × 10−10 +1.60 × 10−19

23.50 × 107 6.20 × 10−19 +1.60 × 10−19

Deduce which sample, 1 or 2, contains a greater percentage of isotope Y.

[3 marks]

Mark scheme

Show the mark scheme A mark scheme showing the accepted answers and guidance for parts 04.1 through 04.5, detailing specific calculations, comparisons of nucleon numbers and specific charges, and methods for deducing the isotopic percentages.

Question Answers Additional Comments/Guidance Mark

details

(mass of ion = ) 1.8(4) × 10–26 (kg)

AO2.1b

04.1 1

(Mass of ion divided by mass of nucleon=) 10.6 or 10.8 ECF allow 1 mark for 10 seen as final answer

04.2 2 AO2.1b

(number of nucleons= ) 11 ECF whole number not in standard form AO2.1b

Allow ‘same proton number’ but not same

‘atomic number’

Allow: isotopes have same number of protons

Same number of protons

AO1.1a

Condone any mention of electrons

AO2.1a

04.3 2

‘ X has more nucleons’ or ‘Y has fewer

X has more neutrons (than Y)

nucleons’ insufficient

Or

Y has fewer neutrons (than X)

7407_1 Version post-stand

ID

details

Specific charge on ion X is less than specific charge on Y

Or

Specific charge on ion Y is greater than specific charge on X

Specific charge is inversely proportional to mass (for the same

charge)

Or words to that effect

04.4 Where equation is stated, the symbols must be 2 AO2.1a

defined or standard symbols must be used. AO2.1a

– SICS – – JUNE 2020

Specific charge of sample determined correctly

Specific charge of each sample determined correctly

Sample 2 has a greater percentage because it has a higher specific

charge

Or

Mean mass of a nucleon in a sample determined correctly Mean mass of a nucleon sample 1=

Mean mass of a nucleon in each sample determined correctly 1.8 x 10–26 kg

Sample 2 has a greater percentage because the nucleons have a

lower mean mass.

Mean mass of a nucleon sample 2 =

1.77 x 10–26 kg

Or

Mean mass of a nucleon in a sample determined correctly

Specific charge of sample 1 = 8.8 x 106 (C kg–1)

Multiples by this average by number of nuclei in the other sample AO3.1a

04.5 Sample 2 has a greater percentage because the nucleons in sample 3 AO3.1a

Specific charge of sample 2 = 9.0 x 106 (C kg–1)

2 have a lower average mass. Or AO3.1a

Sample 2 because it has a lower mass if both samples had the same

number of ions Conclusion must be supported by at least one

relevant, correct calculation

Or Condone one power of ten error in one calculation.

Accept converse statements.

109 times smaller in number but more than 109 times smaller mass Condone incorrect units

(Therefore) sample 2 must have a lower mean mass (than sample

1)

Sample 2 has a greater percentage of Y because Y has less mass

than X

Total 10

How to answer it

Specific Charge and Nuclear Composition of Isotopes

AQA AS Level Physics • Particles

What this question tests

This question assesses your understanding of fundamental particle properties, specifically specific charge (charge-to-mass ratio), isotopic nuclear structure (protons and neutrons), and data analysis involving macroscopic samples of elements. You will need to manipulate the specific charge equation, apply standard atomic mass approximations, and logically deduce isotopic compositions from experimental sample data.

Part (0.4.1) - Calculating the Mass of an Ion

💡 Key Knowledge

  • Specific charge is defined as charge per unit mass: Specific Charge = Charge / Mass
  • Rearranging for mass gives: Mass = Charge / Specific Charge

📐 Calculation Steps

  1. Identify values: Charge ( Q ) = +1.6 × 10⁻¹⁹ C, Specific Charge ( s ) = 8.7 × 10⁶ C kg⁻¹.
  2. Rearrange formula: m = Q / s
  3. Substitute numbers: m = (1.6 × 10⁻¹⁹) / (8.7 × 10⁶)
  4. Calculate result: 1.84 × 10⁻²⁶ kg

✅ Correct Answer

1.8 × 10⁻²⁶ kg (or 1.84 × 10⁻²⁶ kg )

Awarded 1 mark for the correct numerical value and unit.

Part (0.4.2) - Determining Nucleon Number

🧠 Exam Technique

To find the total number of nucleons (protons + neutrons), divide the total mass of the ion by the average mass of a single nucleon. Remember to round your final answer to the nearest whole number, as nucleon numbers must be integers.

📐 Calculation Steps

  1. Mass of ion from 04.1: ~1.84 × 10⁻²⁶ kg (or use unrounded value 1.839 × 10⁻²⁶).
  2. Mass of single nucleon: 1.7 × 10⁻²⁷ kg.
  3. Divide: (1.84 × 10⁻²⁶) / (1.7 × 10⁻²⁷) = 10.8
  4. Round to integer: 11 nucleons.

❌ Common Errors

Students frequently lose the second mark by leaving their answer as a decimal (e.g., 10.8) or failing to round to the nearest whole integer. A nucleon count must be a discrete whole number.

Awarded 2 marks: 1 for the division calculation (allowing ECF from 04.1), and 1 for rounding correctly to 11.

Part (0.4.3) - Comparing Nuclear Compositions

💡 Key Knowledge

Isotopes are atoms of the same element that have the same number of protons (proton number / atomic number) but a different number of neutrons.

✅ Correct Answer

  • Both isotopes have the same number of protons.
  • X has more neutrons than Y (since a nucleus of X has more mass than Y).
Awarded 2 marks. Note: Saying "X has more nucleons" is insufficient on its own because it does not explicitly clarify the neutron difference required for isotopes.

Part (0.4.4) - Comparing Specific Charges of Isotopes

💡 Key Knowledge

Since both ions carry the identical net charge (+1.6 × 10⁻¹⁹ C) but isotope X has a larger mass than isotope Y, its charge-to-mass ratio must be lower.

✅ Correct Answer

  • The specific charge on ion X is less than the specific charge on ion Y.
  • Explanation: Specific charge is inversely proportional to mass (for an equal ionic charge).
Awarded 2 marks: 1 for the correct comparison statement, and 1 for stating the inverse proportionality or explaining via the mass difference.

Part (0.4.5) - Deducing Isotope Abundance in Samples

🧠 Exam Technique

This is a high-tariff synoptic question. To determine which sample has a greater percentage of isotope Y (the lighter isotope), calculate either the average specific charge of the sample or the mean mass per ion for each sample.

📐 Step-by-Step Analysis

  1. Find total mass per ion: Divide total sample mass by the number of ions.
    • Sample 1: (6.31 × 10⁻¹⁰) / (3.50 × 10¹⁶) = 1.80 × 10⁻²⁶ kg
    • Sample 2: (6.20 × 10⁻¹⁹ / 3.50 × 10⁷) [Note data scaling] -> Mean mass = 1.77 × 10⁻²⁶ kg
  2. Compare masses: Sample 2 has a smaller mean mass per ion, meaning it contains a higher proportion of the lighter isotope Y.

✅ Correct Answer

Sample 2 contains a greater percentage of isotope Y.

Awarded 3 marks: 1 for determining sample parameters correctly, 1 for consistent numerical comparison, and 1 for linking lower mass / higher specific charge to a higher percentage of isotope Y.

Topics

Physics · 3.2 Particles and radiation

Question and mark scheme from the AQA AS Level Physics examination, Paper 1, November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.