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If the kinetic energy of an electron gets doubled, its de Broglie wavelength will become _________.
1. doubled
2. (1/√2) times
3. squared
4. √2 times

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Correct Answer - Option 2 : (1/√2) times

CONCEPT:

  • de Broglie wavelength of electrons: Louis de Broglie theorized that not only light possesses both wave and particle properties, but rather particles with mass - such as electrons - do as well.
    • The wavelength of material waves is also known as the de Broglie wavelength.
  • de Broglie wavelength (λ) of electrons can be calculated from Planks constant h divided by the momentum of the particle.

λ = h/p

where λ is de Broglie wavelength, h is Plank's const, and p is the momentum.

  • In terms of Energy, de Broglie wavelength of electrons:

\(λ=\frac{h}{\sqrt{2mE}}\)

where λ is de Broglie wavelength, h is Plank's const, m is the mass of an electron, and E is the energy of the electron.

CALCULATION:

Given that E2 = 2E1

\(λ_1=\frac{h}{\sqrt{2mE_1}}\)       .....(i)

\(λ_2=\frac{h}{\sqrt{2mE_2}}\)       .....(ii)

\(\frac{λ_1}{λ_2}=\sqrt\frac{E_2}{E_1}=\sqrt\frac{2E_1}{E_1}\)

\(\frac{λ_2}{λ_1}=\sqrt\frac{1}{2}\)

\({λ_2}={λ_1}\frac{1}{\sqrt2}\)

So the correct answer is option 2.

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