The de Broglie wavelength associated with a proton under the influence of an electric potential of 100 volts…

The de Broglie wavelength associated with a proton under the influence of an electric potential of 100 volts is
  1. 1.227 Å
  2. 2.86pm
  3. 12.27 Å
  4. 1.146×10-21 m

Solution

From the conservation of energy, 12mv2=eV

⇒p22m=eV

⇒p2=2meV

⇒p=2meV

Wavelength, λ=hp

⇒λ=h2meV

⇒λ=6.625×10-342×1.67×10-27×1.6×10-19×100

⇒λ=6.625×10-342×1.67×10-27×1.6×10-19×100

⇒λ=2.86 pm

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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