Question about the Heisenberg Uncertainty Principle

  • Thread starter MrDMD83
  • Start date
  • #1
25
0

Homework Statement



Suppose the minimum uncertainty in the position of a particle is equal to its de Broglie wavelength. If the particle has an average speed of 4.7 105 m/s, what is the minimum uncertainty in its speed?

Homework Equations



lambda=h/p & (Py)(Y) is greater than or equal to h/4pi

The Attempt at a Solution



I'm not really sure where to start
 

Answers and Replies

  • #2
Let LAMDA = De Broglie Wavelength
DELTAp = uncertainty in linear momentum
DELTAy = uncertainty in position
DELTAv = uncertainty in speed

(Question gives:) DELTAy = LAMDA
Since DELTAp*DELTAy = h/(4pi), then DELTAp*LAMDA = h/(4pi)
Thus, LAMDA = h/(4pi*DELTAp)

Also, LAMDA = h/p

Combine the 2: h/(4pi*DELTAp) = h/p
So: 4pi*DELTAp = p

p = mv, DELTAp = m*DELTAv
4pi*m*DELTAv = mv
4pi*DELTAv = v

We want DELTAv, so:
DELTAv = v/(4pi)

tada.
 
  • #3
1
0
oh man, delta p=m*delta v was the whole key to figuring this out that I NEVER would have thought of. Thank you so much for this detailed solution!! You are the master :)
 

Related Threads on Question about the Heisenberg Uncertainty Principle

Replies
1
Views
162
Replies
3
Views
6K
Replies
5
Views
4K
Replies
2
Views
5K
  • Last Post
Replies
6
Views
2K
Replies
1
Views
3K
  • Last Post
Replies
0
Views
993
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
894
Replies
0
Views
2K
Top