Textbook #1B.23

[Ziyi Meng 2K]

Hi,

"What is the minimum uncertainty in the speed of an electron confined within a lead atom of diameter 350. pm? Model the atom as a one-dimensional box with a length equal to the diameter of the actual atom."

Why is the uncertainty in position 350. pm? And can someone explain to me what the Heisenberg uncertainty principle means? Like what does it tell us?

[Jayden Arevalo 2B]

The 350 pm represents your change in position (delta x). Convert this to meters using the pm to m conversion rate. Then substitute your change of momentum (delta p) to m*delta v which represents mass times change in velocity. In this case, want change in velocity (speed), so isolate the change in velocity and solve. You should get 1.65*10^5 m/s as your change in speed (delta v).

[sgarza]

Hi,

"What is the minimum uncertainty in the speed of an electron confined within a lead atom of diameter 350. pm? Model the atom as a one-dimensional box with a length equal to the diameter of the actual atom."

Why is the uncertainty in position 350. pm? And can someone explain to me what the Heisenberg uncertainty principle means? Like what does it tell us?

This is referring to the atom in a box model. The atom in a box model means that the uncertainty in distance is equivalent to the diameter of the atom, in this case, the lead atom.
The heisenberg uncertainty principle simply states that for objects of small mass (like electrons), there is a limit in the accuracy in which the actual speed and position of the electron can both be known at the same time. The uncertainty in position is the spread of values that could possibly be the distance. This is true for the velocity as well.