Chemistry, asked by ashishyadavrai652, 8 months ago

What is minimum uncertainty in the velocity of a bullet weighing 0.01kg whose position is known with +_1x10-5m accuracy

Answers

Answered by msjayasuriya4
0

Answer:

Using Heisenberg's uncertainty principle, how would you calculate the uncertainty in the position of a 1.60mg mosquito moving at a speed of 1.50 m/s if the speed is known to within 0.0100m/s?

Chemistry Heisenberg Uncertainty Principle

1 Answer

Stefan V.

Nov 8, 2015

3.30

10

27

m

Explanation:

The Heisenberg Uncertainty Principle states that you cannot simultaneously measure both the momentum of a particle and its position with arbitrarily high precision.

Simply put, the uncertainty you get for each of those two measurements must always satisfy the inequality

Δ

p

Δ

x

h

4

π

, where

Δ

p

- the uncertainty in momentum;

Δ

x

- the uncertainty in position;

h

- Planck's constant -

6.626

10

34

m

2

kg s

1

Now, the uncertainty in momentum can be thought of as the uncertainty in velocity multiplied, in your case, by the mass of the mosquito.

Δ

p

=

m

Δ

v

You know that the mosquito has a mass of

1.60 mg

and that the uncertainty in its velocity is

Δ

v

=

0.01 m/s

=

10

2

m s

1

Before plugging your values into the equation, notice that Planck's constant uses kilograms as the unit of mass.

This means that you will have to convert the mass of the mosquito from miligrams to kilograms by using the conversion factor

1 mg

=

10

3

g

=

10

6

kg

So, rearrange the equation to solve for

Δ

and plug in your values

Δ

x

h

4

π

1

Δ

p

=

h

4

π

1

m

Δ

v

Δ

x

6.626

10

34

m

2

kg

s

1

4

π

1

1.60

10

6

kg

10

2

m

s

1

Δ

x

0.32955

10

26

m

=

3.30

10

27

m

The answer is rounded to three sig figs.

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