CK-12-Physics - Intermediate

http://www.ck12.org Chapter 24. Atomic Physics

FIGURE 24.10

Treating light as an uncertain particle.

http://www.youtube.com/watch?v=a8FTr2qMutA

Illustrative Example 25.3.1

a. The uncertainty in the momentum of an electron is given as∆p= 1. 54 × 10 −^27 kg−sm. What is the minimum
uncertainty in its position if both measurements are attempted simultaneously?

Solution:

∆x∆p≥

h

2 π

→∆x

(

1. 54 × 10 −^27

kg−m

s

)

≥

6. 626 × 10 −^34 J−s

2 π

→

∆x≥ 6. 847 × 10 −^8 → 6. 85 × 10 −^8 m

Therefore, the minimum uncertainty is 6. 85 × 10 −^8 m.

b. How many times larger is∆xcompared to the radius of the Bohr radius?

Solution:

The Bohr radius isr 1 = 0. 529 × 10 −^10 m. Thus,
6. 85 × 10 −^8 m
0. 529 × 10 −^10 m=^1 ,^295