
Interpretation:
The uncertainty in the position of the electron with given speed is to be determined, a comment on the result is to be stated, and the uncertainty in the position of the ball is to be determined.
Concept introduction:
Heisenberg gave the uncertainty principle, which statethat the product of the uncertainty in position and momentum of a particle cannot be less than
It is represented as follows:
Here,
As momentum is the product of mass and velocity, the equation of Heisenberg uncertainty principle can also be represented as shown below:
Here,
The minimum uncertainty in speed is calculated by using the following relation:
The uncertainty in momentum can be evaluated as
The relationship between
The conversion factor is

Answer to Problem 116AP
Solution:
(a)
(b)
Explanation of Solution
a)The minimum uncertainty in an electron’s position
The mass of the electron is
The radius of a hydrogen atom is
The speed of the electron is
The uncertainty in speed can be evaluated as
So, the uncertainty in the speed of the electronis
The uncertainty in the position of theelectron can be evaluated as
Therefore, the uncertainty in the position of the electronis
Since the value for
The momentum of
b) Uncertainty in baseball’s position.
The momentum of
The uncertainty in momentum can be evaluated as
So, the uncertainty in the momentum of the baseball is
The value for
Therefore, the value for
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Chapter 6 Solutions
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