Question

According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the speed of an electron known to located within 1.0nm of the nucleus of a hydrogen atom?

A. 1.1*10E7 m/s

B.5.8*10E4 m/s

C.320m/s

D.32m/s

E.0.058m/s

F.1.1*10E-4m/s

G.5.8*10E-5m/s

H.2.9*10E-8m/s

I.5.3*10E-26m/s

J.4.8*10E-56m/s

Answer 1

Given that:

Uncertainty in position, ΔX = 1 nm = 10^-9 m

Mass of electron, m = 9.11 x 10^-31 kg

Hence, According to Heisenberg's uncertainty principle, uncertainty in the speed of an electron will be:

ΔV = h/(4πmΔx)

ΔV = (6.626 x 10^-34) / (4π* 9.11 x 10^-31 * 10^-9 m)

ΔV = 5.8 x 10⁴ m/s ----------- (answer)

• So the correct option is: option (B) 5.8 x 10⁴ m/s