Calculate velocity of an electron having de Broglie's wavelength 58 nm and mass 9.1 10⁻³¹ ~kg ? [ ~h =6.63 10⁻³⁴ Js ]

Step-by-step solution

Velocity from de Broglie wavelength The de Broglie wavelength formula relates a particle's wavelength to its momentum: = h / (mv) . Solving for velocity: v = h / (m ) Given = 58 10⁻⁹ m, m = 9.1 10⁻³¹ kg, and h = 6.63 10⁻³⁴ J·s: v = 6.63 10⁻³⁴ (9.1 10⁻³¹)(58 10⁻⁹) The denominator simplifies to 527.8 10⁻⁴⁰ kg·m, yielding: v = 6.63 10⁻³⁴ 527.8 10⁻⁴⁰ = 0.01256 10⁶ = 1.256 10⁴ m/s Rounded to three significant figures: v = 1.26 10⁴ m/s, which corresponds to option C.