sionId":"05e2aa39-2ba3-4d9f-ac62-1d8e6f68a029","questionNumber":null,"questionType":"LA","specification":"","difficulty":4,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"5d75b0de-774b-4ff7-bcc6-5e1314737d14","label":null,"content":"A deep-space probe uses radio waves to transmit data back to Earth. The radio waves have a wavelength of \$6.0\\text{ cm}\$. The speed of radio waves through space is \$3.0 \\times 10^8\\text{ m/s}\$. Calculate the frequency of the radio waves. Give your answer in standard form.","markscheme":"- Converts wavelength to metres: $\\lambda = 6.0\\text{ cm} = 0.060\\text{ m}$ or $6.0 \\times 10^{-2}\\text{ m}$ B1\n- Rearranges the wave equation to $f = \\frac{v}{\\lambda}$ and substitutes the given values: $f = \\frac{3.0 \\times 10^8}{0.060}$ M1\n- Calculates the frequency as $5.0 \\times 10^9\\text{ Hz}$ in standard form A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"wave_equation","label":"Use the wave equation","steps":[{"type":"text","order":0,"title":"Convert the wavelength","content":"The wave equation uses SI units, so wavelength must be in metres. Since $1\\text{ cm}=0.01\\text{ m}$,\n\n$$\\lambda=6.0\\text{ cm}=0.060\\text{ m}=6.0\\times10^{-2}\\text{ m}$$\n\nThis conversion earns the **B1** mark.","highlights":[{"text":"wavelength of \$6.0\\text{ cm}\$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=wave-equation}{v=f\\lambda}"},{"latex":"\\htmlData{anchor=frequency-form}{f=\\frac{v}{\\lambda}}"},{"latex":"f=\\frac{3.0\\times10^{8}}{\\htmlData{anchor=wavelength-value}{0.060}}"}],"highlights":[{"color":"sky","style":"underline","anchor":"wavelength-value"}],"connections":[{"to":"frequency-form","from":"wave-equation","color":"amber","label":"divide by wavelength"}]},"order":1,"title":"Rearrange and substitute","description":"Start with the wave equation. Divide both sides by wavelength to make frequency the subject. Examiner note: rearranging to frequency equals speed divided by wavelength and substituting 3.0 times 10 to the power of 8 and 0.060 earns the M1 mark."},{"type":"text","order":2,"title":"State the frequency","content":"Evaluating the division gives\n\n$$f=5.0\\times10^{9}\\text{ Hz}$$\n\nThis is already in standard form: the first number is at least $1$ and less than $10$. This correct calculation and unit earn the **A1** mark.","highlights":[{"text":"Give your answer in standard form.","location":"specification"}]}]}],"generatedAt":"2026-07-22T09:23:29.665Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"6acf2d54-9230-4238-9921-21ce432cc40f","revisionId":"f4320f40-bed7-44b7-a5e2-282f8fc91ad0","questionNumber":null,"questionType":"LA","specification":"An optical inspection system uses a converging lens to project a magnified, real image of a microchip defect onto a digital sensor, as shown in the diagram below.\n\n![Microchip defect imaging setup](https://assets.mathsgenie.co.uk/aqa-qb/439cfcfb-4088-44cf-99a8-4373832a663b.png)\n\nThe active vertical span of the sensor is $12.8\\text{ mm}$, and the image of the defect exactly spans this height (so the image height $h_i = 12.8\\text{ mm}$).\n\nThe optical configuration produces a linear magnification of $16.0$.","difficulty":4,"difficultyBand":"medium","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"a8ccebb9-7de1-4fb0-81f8-267c58ab2515","label":null,"content":"Calculate the actual height, $h_o$, of the microchip defect. Give your answer in micrometres ($\\mu\\text{m}$).","markscheme":"- Recalls or uses the magnification formula: $\\text{Magnification} = \\frac{\\text{image height}}{\\text{actual height}}$ (or $M = \\frac{h_i}{h_o}$) M1\n- Rearranges the formula to express the actual height of the defect: $h_o = \\frac{12.8\\text{ mm}}{16.0}$ M1\n- Calculates the actual height in millimetres:

Electromagnetic waves

Question 13

Electromagnetic waves Questions

Electromagnetic waves

Question 13

Electromagnetic waves Questions