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Question
An electron, a proton, an α-particle, and a hydrogen atom are moving with the same kinetic energy. The associated de Broglie wavelength will be longest for ______.
Options
Electron
Proton
α-particle
Hydrogen atom
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Solution
An electron, a proton, an α-particle, and a hydrogen atom are moving with the same kinetic energy. The associated de Broglie wavelength will be longest for electron.
Explanation:
The equation which relates Kinetic energy and De Broglie wavelength is `lambda = h/sqrt(2mE)`
- According to the given condition, kinetic energy E is the same for all the given particles.
- So, the value of the de Broglie wavelength depends on the mass of the particle. If the mass of the particle is more, then de Broglie's wavelength is lower, and vice versa.
- Among the given particles, the electron has the lowest mass in the order of 9.1 × 10−31 kg.
- Therefore, the electron has the longest de Broglie wavelength.
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