1B #25

[Deena Doan 2F]

Hi,
Can someone please explain this problem to me? I don't understand it.

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.

Thank you!

[ariaterango_1A]

Hi! So the uncertainty equation states that uncertainty in momentum (delta p) * the uncertainty in position (delta x) is greater than or equal to h/4pi. So first we convert 350 pico-meters to meters which is your delta x. Then you calculate (6.626 x10^-34)/ (4)*(3.14)*(350 x10^-12m) to find the uncertainty in momentum Then we use the equation uncertainty in momentum (delta p)= mass (of an electron) * uncertainty in velocity to calculate the velocity of 1.65x10^5 m.s^-1.