r=answer}{\\color{@green}{125\\text{ nm}^{3}}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"sides"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"sides","color":"green","label":"multiply"}]},"order":1,"title":"Multiply the three sides","description":"Use the side length three times because a cube has three perpendicular dimensions.\n\nB1: uses all three 5 nm dimensions and gives 125 nm³."}]}],"generatedAt":"2026-07-21T04:26:34.159Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"89dbb1cd-c1fd-4fba-8d82-7c9594507d29","label":"c","content":"The simplest whole-number ratio of \$\\text{surface area} : \\text{volume}\$ for the cubic nanoparticle.\n\nUse the equation:\n\\[\\text{surface area of cubic nanoparticle} = 6 \\times \\text{surface area of one face}\\]","markscheme":"- Sets up the ratio of surface area to volume: $150 : 125$ M1\n- Simplifies to the lowest whole-number ratio: $6 : 5$ A1","marks":2,"order":2,"markingRubric":null,"explanation":{"methods":[{"id":"area_volume_ratio","label":"Calculate then simplify","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{area of one face}=5\\text{ nm}\\times5\\text{ nm}=25\\text{ nm}^{2}"},{"latex":"\\text{surface area}=6\\times25\\text{ nm}^{2}=150\\text{ nm}^{2}"},{"latex":"\\text{volume}=5\\text{ nm}\\times5\\text{ nm}\\times5\\text{ nm}=125\\text{ nm}^{3}"},{"latex":"\\text{surface area}:\\text{volume}=150:125"}]},"order":1,"title":"Form the unsimplified ratio","description":"Find the area of one square face, then use the given equation for the total surface area. Calculate the volume separately before writing the ratio; this earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=original}{150:125}"},{"latex":"\\htmlData{anchor=divided}{\\frac{150}{25}:\\frac{125}{25}}"},{"latex":"\\htmlData{anchor=answer}{6:5}"}],"connections":[{"to":"divided","from":"original","color":"sky","label":"divide both parts by 25","style":"solid"}]},"order":2,"title":"Simplify the ratio","description":"Both parts have a highest common factor of 25, so divide both by 25. This gives the lowest whole-number ratio and earns the A1 mark."}]}],"generatedAt":"2026-07-21T04:35:32.918Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ad61c4cb-3102-4330-9d60-1183077606a8","revisionId":"212a04aa-d002-4217-b346-3b5cc57b49ba","questionNumber":null,"questionType":"LA","specification":"Titanium dioxide can be produced as nanoparticles. A nanoparticle of titanium dioxide is a cube of side \$74\\text{ nm}\$.\n\n![A line-drawing diagram of a cube representing a nanoparticle. A double-headed horizontal arrow above the top-front edge is labeled 74 nm.](https://assets.mathsgenie.co.uk/aqa-qb/e4aa5d11-c7ed-4f6a-a77d-c4f9d2974056.png)","difficulty":5,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"9068104b-cc06-4c2c-b846-fc922b4c2f07","label":null,"content":"Calculate the surface area of this nanoparticle of titanium dioxide. Give your answer in standard form.","markscheme":"- Calculates the area of one face of the cube: $74 \\times 74 = 5476\\text{ nm}^2$ M1\n- Multiplies by $6$ to find the total surface area: $6 \\times 5476 = 32856\\text{ nm}^2$ M1\n- Converts to standard form to give $3.3 \\times 10^4\\text{ nm}^2$ (or $3.2856 \\times 10^4\\text{ nm}^2$) A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"cube_surface_area","label":"Cube surface area","steps":[{"type":"text","order":0,"title":"Identify the faces","content":"The nanoparticle is a cube. A cube has six identical square faces, each with side length $74\\text{ nm}$.","highlights":[{"text":"A nanoparticle of titanium dioxide is a cube of side \$74\\text{ nm}\$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes"

Bulk and surface properties of matter including nanoparticles (chemistry only)

Question 11

Bulk and surface properties of matter including nanoparticles (chemistry only) Questions

Bulk and surface properties of matter including nanoparticles (chemistry only)

Question 11

Bulk and surface properties of matter including nanoparticles (chemistry only) Questions