GATE 2020 BM – Question 61
Find the de Broglie wavelength in nm of an electron accelerated through 1 V, to two decimals. Use electron mass 9.11×10⁻³¹ kg,h=6.63×10⁻³⁴ J s and electron charge 1.6×10⁻¹⁹ C.
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Correct answer: 1.20 to 1.25
Explanation
The kinetic energy is eV and nonrelativistic momentum is p=√(2meV). Therefore λ=h/√(2meV)=6.63×10⁻³⁴/√(2×9.11×10⁻³¹×1.6×10⁻¹⁹×1)≈1.228×10⁻⁹ m. Converting metres to nanometres gives 1.23 nm.