# If the kinetic energy of an electron gets doubled, its de Broglie wavelength will become _________.

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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.