Question

An electron has a speed of 4*10^5 , accurate to 0.01%. With what fundamental accuracy can we locate the position of electron?

Answer 1

An electron has a speed of 4 ×10^5 , accurate to 0.01%. With what fundamental accuracy can we locate the position of electron?

solution : according to Heisenberg's uncertainty principle

∆x = h/{4πm∆v}

where h is Plank's constant i.e., h = 6.63 × 10^-34 Js

m is mass of electron i.e., m = 9.1 × 10^-31 Kg

∆v is uncertainty in speed of electron i.e., ∆v = 0.01% of 4 × 10^5 = 1/10⁴ × 4 × 10^5 = 40 m/s

now, ∆x = (6.63 × 10^-34)/(4 × 3.14 × 9.1 × 10^-31 × 40)

≈ 1.45 × 10^-6 m

hence, uncertainty in the position of electron is 1.45 × 10^-6 m