How do you calculate the uncertainty in velocity of an electron given position, mass and speed of the electron?

Question

I’m to calculate the uncertainty in the velocity of an electron given the following information:
The electron is moving at 1.0 x 106 m/s
its mass is 9.11 x 10-31 kg.
the position is to be located within 6.4 x 10-12 m.
I know I’m to use the equation (Δx) (Δp) > h/4π(pi)
I believe I know that p = momentum which = mass x velocity =(9.11 x 10-31 kg) (1.0 x 106 m/s) = 9.11 x 10-25 kg·m/s
But I’m given the Δx (position uncertainty) which is 6.4 x 10-12 m, I know h= 6.626 x 10-34 (kg·m2/s2)·s
So I’m stuck not knowing what I’m actually solving for.

 

Clarification needed because unfortunately all the examples in the textbook are not for this type of problem.      

 

Answer 1

Possibly you are to use the Heisenberg Uncertainty Principle as the other answer explains.

But you state you are to use the equation (Δx) (Δp) > h/4π(pi)

Maybe you are being expected to do a standard calculation of measurement uncertainty.

If so ....

 

You cannot calculate the uncertainty to the calculation unless you know the uncertainty of each measurement involved in the equation.

 

Are you to assume that the significant digits are giving you the uncertainty of the measurements?

That is a pretty Big assumption to make.

And personally I wouldn't make any assumptions, and no scientist or engineer would make assumptions, without having a reasonable basis for making them.

 

Check these two resources of mine:

1) http://www.wyzant.com/resources/answers/39373/how_do_you_write_an_expression_of_uncertainty_of_the_spring_constant_by_propagation_of_errors_using_standard_deviation

2) http://www.wyzant.com/resources/answers/42773/determine_an_expression_for_the_uncertainty_of_the_equivalent_capacitance_of_this_circuit

 

To use the equation (Δx) (Δp) > h/4π(pi)

You need to know the uncertainties for all the components in the equation:

Δx , Δp , h , pi n , and 4

  (4 and n are constants so uncertainty = 0 for those)

 

 

Answer 2

Warning I have no idea if this is correct as it is outside my areas of study.  But

Heisenberg's Uncertainty Principle says: σ_xσ_p≥h/2 where h is Planck's Constant and σ is the standard deviation of position (x) and momentum (p).

So it would seem to me that the it is just algebra 1 stddev of momentum is σ_p≥h/(2σ_x) and p=mv and assuming the mass is constant (an assumption I am not sure of in this context) then the uncertainty of the velocity would be σ_p/mass or σ_v≥(h/(2σ_x*mass).  

Switching to the definition you provided σ_v≥(h/(4πσ_x*mass) or 

σv≥(6.626x10^-34(kg·m²/s²)·s)/(4*π*6.4x10^-12 m*9.11x10^-31kg)

9.04x10⁶m/s Which looks wrong to me even though the units work out :(