Question

What is the linear size of the smallest box in which you can confine an electron if you want to know for certain that the electron's speed is no more than 13 m/s ? Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

the linear size of the smallest box in which you can confine an electron

=7 μm

Explanation:

From the uncertainity principle we can write that

$\Delta p\Delta x = \frac{h}{4\pi}$

x= position of electron

p= momentum of electron

h= planks constant

$\Delta x= \frac{h}{2\pi\times2m\Delta v}$

here the moving of electron will taken two times

as the electrons are going and reflected from the wall of the box

so the velocity Δv= 2*13= 26 m/s

now putting the values of all the variables in the above equation

$\Delta x= \frac{6.625\times10^{-34}}{2\pi\times2(9.1\times10^{-31})26}$

⇒Δx= 7×10^{-6} m

=7 μm