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What is the de Broglie wavelength associated with an electron moving with a speed of 6.4×10⁶ m s⁻¹? (Mass of electron mₑ = 9.11×10⁻³¹ kg, Planck's constant h = 6.63×10⁻³⁴ J s)

Asked in GUJCET 2022 · de Broglie relation and its graphs

• (1) 0.124 nm
• (2) 0.114 nm
• (3) 0.135 nm
• (4) 0.145 nm

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 0.124 nm; it would need a speed of about 5.9×10⁶ m s⁻¹. Here mₑv = 5.83×10⁻²⁴ kg m s⁻¹, which gives 0.114 nm.
• (3) 0.135 nm is the familiar textbook value for an electron at 5.4×10⁶ m s⁻¹, recalled rather than worked out for 6.4×10⁶ m s⁻¹.
• (4) No single slip gives 0.145 nm; it would need a speed of about 5.0×10⁶ m s⁻¹, and a faster electron has a shorter wavelength than that.

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