Physics · Matter waves: wave nature of particle, de-Broglie relation
The energy that should be added to an electron to reduce its de-Broglie waveleng
The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is.
- A. Four times the initial energy
- B. Equal to the initial energy
- C. Twice the initial energy
- D. Thrice the initial energy
Step-by-step solution
The de Broglie wavelength λ = h/p, and for non-relativistic electron kinetic energy E = p²/(2m), so λ ∝ 1/√E. Halving λ requires quadrupling E. Thus final energy = 4 × initial energy, so added energy = 3 × initial energy.
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