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Physics / Physics with MasteringPhysics 4 / Chapter 30 / Problem 77P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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The uncertainty in an electron’s position is 0.15 nm. (a)

Chapter 30, Problem 77P

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QUESTION:

Problem 77P

The uncertainty in an electron’s position is 0.15 nm. (a) What is the minimum uncertainty ∆p in its momentum? (b) What is the kinetic energy of an electron whose momentum is equal to this uncertainty (∆p = p)?

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QUESTION:

Problem 77P

The uncertainty in an electron’s position is 0.15 nm. (a) What is the minimum uncertainty ∆p in its momentum? (b) What is the kinetic energy of an electron whose momentum is equal to this uncertainty (∆p = p)?

ANSWER:

Step 1 of 2

a)

Here, we have to find the minimum uncertainty in the momentum of the particle.

Given that,

$\Delta{}x=0.15\ nm$

We know that,

$\Delta{}x\Delta{}p\geq{}\frac{h}{2\pi{}}$

$\Rightarrow{}\Delta{}p\geq{}1.03\times{}1{0}^{-33}/\left({0.15\times{}1{0}^{-9}}\right)$

$\Rightarrow{}\Delta{}p\geq{}6.8\times{}1{0}^{-25}$

So, the smallest uncertainty in momentum is $6.8\times{}1{0}^{-25}\ kg\ m/s$ .

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