When using the Heisenberg uncertainty principle, and you are seeking to find delta x, and are given both the velocity and delta v, does the velocity even matter? The equation only states that h/ (4 times pi times mass times delta v) = delta x.
you have the formula correct. in acatuality, delta V is greater with greater velocity (measurements are precise to only so many digits)
So for example, if there was an electron mass of 6.24 times 10^-20 kg, moving at a velocity of 4.5 times 10^8 m/s, and we were given delta v as .01 times 10^8 m/s, the equation would be
h/ (4 times pi times (6.24 times 10^-20) times (.01 times 10^8))
or do we plug in 4.5 times 10^8?
No. v doesn't matter.
When using the Heisenberg uncertainty principle to find delta x (the uncertainty in position), you are correct that the equation you mentioned is used: delta x * delta v >= h / (4πm).
In this equation, h represents the Planck constant, which is a fundamental constant in quantum mechanics. The mass of the particle in question is denoted by m.
Now, as for your question about the velocity (v), it is important to note that velocity does not directly appear in the Heisenberg uncertainty principle equation. The uncertainty in velocity, delta v, is related to the uncertainty in position, delta x.
The equation suggests that there is an inherent trade-off between the uncertainties of position and velocity for a particle. The more precisely you try to measure the position (smallest delta x), the greater the uncertainty in velocity (larger delta v) becomes, and vice versa. This is a fundamental aspect of quantum mechanics.
However, even though velocity does not explicitly appear in the equation, it is indirectly connected to the uncertainty principle through the mass of the particle. The mass (m) of an object affects its momentum, and momentum is related to velocity according to the formula p = mv, where p is momentum.
So, even though the equation does not directly reference velocity, it indirectly involves it through the mass term. It tells us that it is impossible to simultaneously measure the exact position and velocity of a particle to arbitrary precision due to the inherent uncertainty in quantum mechanics.