Use the Heisenberg uncertainty principle to calculate the uncertainty (in meters) in the position of a honeybee weighing 0.67 g and traveling at a velocity of 0.80 m/s . Assume that the uncertainty in the velocity is 0.1 m/s.

9.84x 10^-31m

Explanation: 9.84x 10^-31m

Heisenberg uncertainty principle states that  says that the position and momentum of a particle cannot be known at the same time and accurately. and that the values  of position and momentum all times must be greater than h/4π.

Using the formula for Heisenberg Uncertainty principle

Δx. Δp ≥ h / 4π

=Δx. m ΔV ≥ h / 4π

where h = Planck’s constant = 6.62607004 × 10-34 m2 kg / s

Δx is the uncertainty in position

Δp is the uncertainty in momentum

m = mass

Δv=is the uncertainty in velocity

Given,

v = 0.80m/s,

m = 0.67 g = 0.67 g / 1000

= 0.00067 kg

h = 6.62607004 × 10-34 m2 kg / s

uncertainty in the velocity is 0.1 m/s.

Δv = 0.80×0.1 = 0.080m/s

Δx. m ΔV ≥ h / 4π

Δx  ≥ h / 4πm ΔV

6.62607004 × 10-34 / 4 π x 0.08 x 0.00067

=6.62607004 × 10-34 / 4 x3.14  5.3 x 10^-5 = 9.84x 10^-31m

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