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The de Broglie wavelength of a particle moving with velocity 2.25×10⁸ m s⁻¹ is the same as the wavelength of a photon. The ratio of the kinetic energy of the particle to the energy of the photon is ______. (Velocity of light c = 3×10⁸ m s⁻¹)

Asked in RS Academy GUJCET booklet · Matter wave against photon

• (1) 1/8
• (2) 3/8
• (3) 5/8
• (4) 7/8

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 1/8. Sanity check: the ratio works out to v/(2c), and (2.25)/(2×3) = 0.375 = 3/8.
• (3) 5/8 = 1 - 3/8 is (E-K)/E, the share of the photon's energy left over after subtracting the particle's kinetic energy, not the ratio K/E.
• (4) No single slip gives 7/8. Since K/E = v/(2c) and v < c, the ratio is always below 1/2, so 7/8 is impossible.

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