{"id":110,"date":"2026-06-17T18:08:44","date_gmt":"2026-06-17T18:08:44","guid":{"rendered":"https:\/\/flowxiom.com\/?p=110"},"modified":"2026-06-17T18:09:08","modified_gmt":"2026-06-17T18:09:08","slug":"a-level-ial-unit-1-01-quantities-si-units-2","status":"publish","type":"post","link":"https:\/\/flowxiom.com\/?p=110","title":{"rendered":"A-Level IAL Unit 1 02 Estimation of Physical Quantities"},"content":{"rendered":"\n

Unit 1 02 Estimation of Physical Quantities<\/h2>
<\/div><\/div>
<\/div>

1. Learning Objectives<\/h3><\/div>
    \n
  • <\/span>Subject Content:<\/strong>\n
      \n
    • <\/span>Estimate the approximate order of magnitude for length, time, and mass.
      \n<\/li>\n
    • <\/span>Develop a “mental scale” for common physical entities.
      \n<\/li>\n<\/ul>\n<\/li>\n
    • <\/span>Language Goals:<\/strong>\n
        \n
      • <\/span>Use phrases like “in the order of…” and “approximately…” to describe scales.
        \n<\/li>\n
      • <\/span>Understand the meaning of “Order of Magnitude”.
        \n<\/li>\n<\/ul>\n<\/li>\n<\/ul><\/div>

        2. Key Terminology<\/h3><\/div>
        \n\n\n\n\n\n\n\n\n\n
        Term<\/strong><\/th>\nNotes<\/strong><\/th>\n<\/tr>\n<\/thead>\n
        Estimation<\/strong><\/td>\nBased on experience\/facts<\/td>\n<\/tr>\n
        Order of Magnitude<\/strong><\/td>\nPowers of 10<\/td>\n<\/tr>\n
        Macroscopic<\/strong><\/td>\nVisible to the naked eye<\/td>\n<\/tr>\n
        Microscopic<\/strong><\/td>\nAtomic or sub-atomic scale<\/td>\n<\/tr>\n
        Half-life<\/strong><\/td>\nTime for half of nuclei to decay<\/td>\n<\/tr>\n
        Cosmological Scale<\/strong><\/td>\nGalaxies and the universe<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>
        <\/div>

        3. Estimation of Length<\/h3><\/div>

        A-level Physics requires mastering the range of lengths from the atomic nucleus to the observable universe:<\/p><\/div>

        \n\n\n\n\n\n\n\n\n\n\n\n\n\n
        Object<\/strong><\/th>\nApproximate Length (m)<\/strong><\/th>\nOrder of Magnitude<\/strong><\/th>\n<\/tr>\n<\/thead>\n
        Diameter of a Nucleus<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Diameter of an Atom<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Diameter of a Red Blood Cell<\/strong><\/td>\n<\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Thickness of Paper<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Height of a Human<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Height of Mt. Everest<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Radius of the Earth<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Earth to Sun (1 AU)<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Observable Universe<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        <\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>
        <\/div>

        4. Estimation of Time<\/h3><\/div>

        The time span ranges from the instantaneous reactions of fundamental particles to the age of the universe:<\/p><\/div>

        \n\n\n\n\n\n\n\n\n\n\n\n\n
        Event<\/strong><\/th>\nTime in Seconds (s)<\/strong><\/th>\nOrder of Magnitude<\/strong><\/th>\n<\/tr>\n<\/thead>\n
        Life of a Short-lived Particle<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Period of Visible Light<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Human Reaction Time<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        One Day<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        One Year<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Human Life Span<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Half-life of Uranium-238<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Age of the Universe<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        <\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>
        <\/div>

        5. Estimation of Mass<\/h3><\/div>
        \n\n\n\n\n\n\n\n\n\n\n\n\n\n
        Object<\/strong><\/th>\nApproximate Mass (kg)<\/strong><\/th>\nOrder of Magnitude<\/strong><\/th>\n<\/tr>\n<\/thead>\n
        Electron<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Proton \/ Neutron<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        DNA Molecule<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        A Mosquito<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        An Apple<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Human Adult<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        Boeing 747<\/strong><\/td>\n<\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        The Earth<\/strong><\/td>\n<\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        The Sun<\/strong><\/td>\n<\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n
        The Milky Way<\/strong><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>
        <\/div>

        6. Checkpoint Exercises<\/h3><\/div>

        Q1.<\/strong> Which estimate is realistic for the frequency of a typical microwave oven?<\/p><\/div>

        A. <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/p><\/div>

        B. <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/p><\/div>

        C. <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/p><\/div>

        D. <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span><\/p><\/div>

        Q2.<\/strong> Estimate the density of an apple<\/strong>. (Hint: Use your mass estimation and estimate its volume).<\/p><\/div>

        Q3.<\/strong> What is the order of magnitude of the number of seconds in a standard 2-year A-level course?<\/p><\/div>

        Q4.<\/strong> A student measures the thickness of 500 sheets of paper as <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>. What is the estimated thickness of one single atom, expressed as a fraction of the thickness of one sheet of paper?<\/p><\/div>

        <\/div>

        Detailed Analysis<\/h3><\/div>

        Q1. Frequency of a typical microwave oven<\/h4><\/div>
          \n
        • <\/span>Analysis:<\/strong> \n
            \n
          • <\/span>Microwaves<\/strong> have a wavelength range approximately between <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span> and <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>. The standard frequency of a household microwave oven is usually 2.45 GHz<\/strong>.
            \n<\/li>\n
          • <\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>.
            \n<\/li>\n
          • <\/span>Comparing options: <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span> is Radio waves, <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span> is close to Infrared, and <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span> is Visible light\/Ultraviolet.
            \n<\/li>\n<\/ul>\n<\/li>\n
          • <\/span>Correct Answer: B<\/strong> (<\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>)
            \n<\/li>\n<\/ul><\/div>
            <\/div>

            Q2. Estimate the density of an apple<\/h4><\/div>
              \n
            • <\/span>Step 1: Estimate Mass (<\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>).<\/strong> An apple is approximately <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>, which is <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>.
              \n<\/li>\n
            • <\/span>Step 2: Estimate Volume (<\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>).<\/strong> An apple can be approximated as a sphere with a radius <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>.\n
                \n
              • <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span>.
                \n<\/li>\n<\/ul>\n<\/li>\n
              • <\/span>Step 3: Calculate Density (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-math><\/mjx-container><\/span>).<\/strong>\n
                  \n
                • <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span>.
                  \n<\/li>\n<\/ul>\n<\/li>\n
                • <\/span>Conclusion:<\/strong> The density of an apple is slightly less than that of water (<\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span>), which explains why apples can float on water.
                  \n<\/li>\n
                • <\/span>Estimated Range:<\/strong> <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span>.
                  \n<\/li>\n<\/ul><\/div>
                  <\/div>

                  Q3. Order of magnitude of seconds in a 2-year course<\/h4><\/div>
                    \n
                  • <\/span>Step 1: Total time in years.<\/strong> <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>.
                    \n<\/li>\n
                  • <\/span>Step 2: Use the shortcut.<\/strong> <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span> (Or use <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>).
                    \n<\/li>\n
                  • <\/span>Step 3: Calculate.<\/strong> <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mtext><\/mjx-math><\/mjx-container><\/span>.
                    \n<\/li>\n
                  • <\/span>Final Answer:<\/strong> Its order of magnitude is <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span><\/strong> (because <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span> is greater than <\/mjx-c><\/mjx-mo><\/mjx-surd><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-box><\/mjx-sqrt><\/mjx-msqrt><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span>. In physics estimations, when the coefficient is greater than <\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span>, the order of magnitude is usually rounded up by one).
                    \n<\/li>\n<\/ul><\/div>
                    <\/div>

                    Q4. Atom thickness vs. Paper thickness<\/h4><\/div>