German physicist Werner Heisenberg related the uncertainty of an object's position (Δx) to the uncertainty in its velocity (Δv)Δx≥h4πmΔvwhere h is Planck's constant and m is the mass of the object. The mass of an electron is 9.11×10−31 kg. What is the uncertainty in the position of an electron moving at 3.00×106 m/s with an uncertainty of Δv=0.01×106 m/s?Δ

5.79*10⁻⁹ m is the uncertainty in the position.

Explanation:

Heisenberg's uncertainty principle assumes that it is not possible to know exactly all the data regarding the behavior of particles. In other words, at the subatomic level, it is impossible to know at the same moment where a particle is, how it moves and what its speed is.

So, Heisenberg's Uncertainty Principle gives a relationship between the standard deviation of an object's position and its momentum.

Δp*Δx= h/(4π)

where

By definition, the momentum of the electron equals the product of its mass and velocity. So, being the mass constant, you can said:

Δp= m*Δv

Replacing in the expresion of the Heisenberg's Uncertainty Principle:

m*Δv*Δx= h/(4π)

Then you know:

Replacing:

*Δx=6.63*10⁻³⁴ kg*m²*s⁻¹/(4π)

Taking π=3.14 and solving:

Δx

Δx=5.79*10⁻⁹ m

5.79*10⁻⁹ m is the uncertainty in the position.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: