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NEET 2026 (Re-neet) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from NEET 2026 (Re-neet)

Q21NEET 2026 · RE-NEETMedium

Matter Waves: de Broglie Wavelength

A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron pep_e to that of photon pPh,pepPhp_{Ph}, \frac{p_e}{p_{Ph}} is:

[Take speed of light =3×108 ms−1= 3 \times 10^{8}\text{ ms}^{-1}, charge of electron =−1.6×10−19 C= -1.6 \times 10^{-19}\text{ C} and mass of electron =9×10−31 kg= 9 \times 10^{-31}\text{ kg} ]

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Answer: (d)

  1. E=20 eV=20×1.6×10−19=3.2×10−18 JE = 20\text{ eV} = 20 \times 1.6 \times 10^{-19} = 3.2 \times 10^{-18}\text{ J}.
  2. Electron: pe=2mE=2×9×10−31×3.2×10−18=2.4×10−24 kg m/sp_e = \sqrt{2mE} = \sqrt{2 \times 9 \times 10^{-31} \times 3.2 \times 10^{-18}} = 2.4 \times 10^{-24}\text{ kg m/s}
  3. Photon: pPh=Ec=3.2×10−183×108≈1.067×10−26 kg m/sp_{Ph} = \dfrac{E}{c} = \dfrac{3.2 \times 10^{-18}}{3 \times 10^8} \approx 1.067 \times 10^{-26}\text{ kg m/s}
  4. pepPh=2.4×10−241.067×10−26=225\dfrac{p_e}{p_{Ph}} = \dfrac{2.4 \times 10^{-24}}{1.067 \times 10^{-26}} = 225
  5. So the answer is (d) 225.
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