What would be the uncertainty in velocity (miles/hr) of a neutron beam particle if the position can be measured within +/- 25 angstroms.
The rest mass of a neutron = 1.67493 X 10^-27 kg or 1.008664904(14) amu.
I know you have to use the heisenberg uncertainty principle: (deltaX)(delta mv) > (or equal to) planck's constant/4pi.
So far I have (+/- 25 A)(1.67493XX 10^-27 kg) > 5.21X10^-34
what do i do now?
I believe you must convert Angstroms to meters.
h = 6.626 x 10^-34 J.s instead of the 5.21 you have. Then solve the equation and convert m/s you get for the answer to mi/hr
Also, consider that the uncertainty is +/- 25 and the total "swing" is 50 Ao.Check my thinking.
To calculate the uncertainty in velocity of a neutron beam particle, you can use the Heisenberg Uncertainty Principle equation:
Δx * Δmv ≥ h/4π
where Δx is the uncertainty in position, Δmv is the uncertainty in momentum (mass times velocity), h is Planck's constant, and π is a mathematical constant approximately equal to 3.14159.
From the given information, the uncertainty in position is ±25 angstroms. However, it is necessary to convert this uncertainty to the SI unit of meters before continuing with the calculation.
1 angstrom = 1 × 10^-10 meters
So, ±25 angstroms becomes ±2.5 × 10^-9 meters.
Now you can substitute the values into the equation:
(±2.5 × 10^-9 meters) * Δmv ≥ (6.62607015 × 10^-34 joule seconds) / (4π)
Simplifying this expression will give you the uncertainty in momentum:
Δmv ≥ [(6.62607015 × 10^-34 joule seconds) / (4π)] / (±2.5 × 10^-9 meters)
Now, you mentioned the rest mass of a neutron, which is given as 1.67493 × 10^-27 kg. To find the uncertainty in velocity (Δv), we need to divide the uncertainty in momentum (Δmv) by the mass of the neutron:
Δv = Δmv / mass of the neutron
Δv ≥ [(6.62607015 × 10^-34 joule seconds) / (4π)] / (±2.5 × 10^-9 meters * 1.67493 × 10^-27 kg)
Calculating this expression will give you the uncertainty in velocity (Δv) in meters per second. To convert this to miles per hour, you can multiply the value by a conversion factor:
1 m/s = 2.23694 miles per hour
Therefore, the final step is to multiply the uncertainty in velocity (Δv) by the conversion factor:
Δv (miles per hour) = Δv (meters per second) * 2.23694
This will give you the uncertainty in velocity of the neutron beam particle in miles per hour.