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A photon has energy of $1 \times 10^{18} \text{ eV}$ - AQA - A-Level Physics - Question 8 - 2020 - Paper 1

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A photon has energy of $1 \times 10^{18} \text{ eV}$. An object of mass 0.03 kg has kinetic energy equal to the energy of the photon. What is the speed of the ob... show full transcript

Worked Solution & Example Answer:A photon has energy of $1 \times 10^{18} \text{ eV}$ - AQA - A-Level Physics - Question 8 - 2020 - Paper 1

Step 1

Calculate the kinetic energy

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Answer

The kinetic energy (KE) of the object is equal to the energy of the photon, which is given as: KE=1×1018 eVKE = 1 \times 10^{18} \text{ eV}.\

To convert eV to Joules, multiply by the conversion factor 1 eV=1.6×10−19 J1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}. Thus, KE=1×1018 eV×1.6×10−19 J/eV=1.6×10−1 J.KE = 1 \times 10^{18} \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = 1.6 \times 10^{-1} \text{ J}.

Step 2

Apply the kinetic energy formula

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The formula for kinetic energy is given by: KE=12mv2,KE = \frac{1}{2} m v^2,
where mm is the mass and vv is the speed of the object. Rearranging this formula to solve for speed gives: v=2KEm.v = \sqrt{\frac{2 KE}{m}}. Substituting in the values: v=2×1.6×10−1 J0.03 kg.v = \sqrt{\frac{2 \times 1.6 \times 10^{-1} \text{ J}}{0.03 \text{ kg}}}.

Step 3

Calculate the speed

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Answer

v=0.320.03=10.6667≈3.26 m/s.v = \sqrt{\frac{0.32}{0.03}} = \sqrt{10.6667} \approx 3.26 \text{ m/s}.
Rounding to a reasonable figure gives approximately 3 m/s3 \text{ m/s}. Therefore, the speed of the object is approximately 3 m/s.

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