A photon and an electron each have energy 20 eV in free space. Find their momentum ratio pₑ/pₚₕ. Take c = 3 × 10⁸ m s⁻¹, e = 1.6 × 10⁻¹⁹ C and mₑ = 9 × 10⁻³¹ kg.
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Question

A photon and an electron each have energy 20 eV in free space. Find their momentum ratio pₑ/pₚₕ. Take c = 3 × 10⁸ m s⁻¹, e = 1.6 × 10⁻¹⁹ C and mₑ = 9 × 10⁻³¹ kg.

G1 Physics · Accepted Answer

Step 1: Convert energy: E = 20 × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻¹⁸ J. Step 2: Nonrelativistic electron momentum is pₑ = √(2mₑE). Step 3: Photon momentum is pₚₕ = E/c. Step 4: Ratio = √(2mₑE)/(E/c) = c√(2mₑ/E). Step 5: Substitute = 3 × 10⁸ × √[(2 × 9 × 10⁻³¹)/(3.2 × 10⁻¹⁸)] = 3 × 10⁸ × 7.5 × 10⁻⁷. Final answer: 225 (Option C).