mptFullMarks":null},{"id":"4957c86e-f5f4-4750-94e1-1baf6ad01e92","revisionId":"ccf8c170-b863-4eb3-b4e7-e9758704345a","questionNumber":null,"questionType":"LA","specification":"A cubical microparticle of zinc oxide (\$\\text{ZnO}\$) has six square faces. The dimensions of this microparticle are \$1.2\\ \\mu\\text{m} \\times 1.2\\ \\mu\\text{m} \\times 1.2\\ \\mu\\text{m}\$.\n\nThis microparticle is processed to break it down into \$8000\$ identical smaller nanocubes, each with dimensions \$60\\text{ nm} \\times 60\\text{ nm} \\times 60\\text{ nm}\$.\n\nCalculate:","difficulty":7,"difficultyBand":"medium","totalMarks":7,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"bc103c2f-9990-4605-9f84-9c5bad6a07c8","label":"a","content":"The total surface area of the original microparticle in \$\\mu\\text{m}^2\$.","markscheme":"- Calculates the area of one face of the original microparticle: $1.2 \\times 1.2 = 1.44\\text{ }\\mu\\text{m}^2$ M1\n- Calculates the total surface area by multiplying by 6: $6 \\times 1.44 = 8.64\\text{ }\\mu\\text{m}^2$ A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"surface_area","label":"Calculate surface area","steps":[{"type":"text","order":0,"title":"Find one face","content":"Each face is a square with side length $1.2\\ \\mu\\text{m}$. Use $\\text{area}=\\text{length}\\times\\text{width}$:\n\n$$\\text{area of one face}=1.2\\times1.2=1.44\\ \\mu\\text{m}^2$$\n\nThis correct area calculation earns **M1**.","highlights":[{"text":"dimensions of this microparticle are \$1.2\\ \\mu\\text{m} \\times 1.2\\ \\mu\\text{m} \\times 1.2\\ \\mu\\text{m}\$","location":"specification"}]},{"type":"text","order":1,"title":"Multiply by six","content":"A cube has six identical square faces, so multiply the area of one face by $6$:\n\n$$\\text{total surface area}=6\\times1.44=8.64\\ \\mu\\text{m}^2$$\n\nTherefore, the total surface area is $\\boxed{8.64\\ \\mu\\text{m}^2}$. This earns **A1**.","highlights":[{"text":"has six square faces","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:55:22.614Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"2bf3193e-c382-4e6c-97b8-fbf0c5fc43af","label":"b","content":"The total combined surface area of the \$8000\$ nanocubes in \$\\mu\\text{m}^2\$.","markscheme":"- Converts $60\\text{ nm}$ to micrometres: $60\\text{ nm} = 0.06\\text{ }\\mu\\text{m}$ OR calculates area of one nanocube in $\\text{nm}^2$ as $6 \\times 60^2 = 21,600\\text{ nm}^2$ M1\n- Calculates the total combined surface area in either unit: e.g., $8000 \\times 6 \\times (0.06)^2$ or $8000 \\times 21,600 = 1.728 \\times 10^8\\text{ nm}^2$ M1\n- Correctly converts to $\\mu\\text{m}^2$ to obtain $172.8\\text{ }\\mu\\text{m}^2$ A1","marks":3,"order":1,"markingRubric":null,"explanation":{"methods":[{"id":"calculate_in_nanometres_first","label":"Calculate in nanometres first","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{surface area of one nanocube}=6\\times\\htmlData{anchor=edge}{\\color{@sky}{60^2}}\\ \\text{nm}^2"},{"latex":"\\text{surface area of one nanocube}=\\htmlData{anchor=one_area}{\\color{@green}{21600\\ \\text{nm}^2}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"edge"},{"color":"green","style":"text-color-with-background","anchor":"one_area"}]},"order":0,"title":"Find one cube's area","description":"Keep the edge length in nanometres. A cube has six square faces, so \$6\\times60^2=21600\\ \\text{nm}^2\$; this earns the first M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{total surface area}=\\htmlData{anchor=cube_count}{\\color{@orange}{8000}}\\times21600\\ \\text{nm}^{2}"},{"latex":"\\text{total surface area}=\\htmlData{anchor=total_nm}{\\color{@green}{172800000\\ \\text{nm}^{2}}}"}],"highlights":[{"color":"orange","style":"text-color","anchor":"cube_count"},{"color":"green","style":"text-color","anchor":"total_nm"}]},"order":1,"title":"Scale up to 8000","description":"Multiply the surfa

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

Question 4

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

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

Question 4

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