BioPHYSICAL chemistry

(b)

=Eψ(x,y,z)

(c)

9.27 Classically, the particle would pass through either one slit or the

other but in quantum mechanics the particle has a wave nature that

represents the combination of passing through both slits.

9.28According to the Heisenberg Uncertainity Principle, the uncertainties

in the two parameters are coupled with the product being at least Z/2.

The interpretation of this result is that the observer interferes with

the object during the measurement. For example, when measuring the

position of an object, the probe hits the object and causes a change

in velocity.

9.29

9.30

9.31 First calculate the uncertainty of the ball’s position:

The probability is estimated by the ratio of Δxand the size of the

glove:

9.32 To experience diffraction, the wavelength of the person must be com-

parable to the size of the opening:

9.33 If an electron were confined to such a small volume then the

uncertainty in the velocity would become very large and the motion

of the electron would be subject to the Heisenberg Uncertainty

Principle.

λ

.

=× = =

×

×

−

−

110

7 66 10^34

m

Js

(6.6 1

h

m 9 0 0kg)−−^18 ××() 1109 ms−^1

Probability

m

m

.

==

×

×

=

−

−

l

Δx

10 10

110

6

5 0 01.

Δ

Δ

x

m

.

==

×

×

−

−

Z

2 9

105 10^34

22

Js

2 (1.05 10 kgg) m s

m

(. )

.

××

−−=×−

05 10

71 10 10^5

1

3

22

0 0

2

3

===→ψψ*d() ()xxx AxxA∫∫ d

a

A

a a

==

3

a^3

1 2

0 0

===→=() ()^2 ()

ψψ*d dxxx AxAa∫∫ ψx

a a

Aa= 1/

−++

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

Z^22

2

2

2

2

2 mx y z^2 xyz

∂

∂

∂

∂

∂

∂

ψ(),, ++=()() ()Axyzψψxyz,, E xyz,,

−++

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

Z^22

2

2

2

2

2 mx y z^2 xyz

∂

∂

∂

∂

∂

∂

ψ(),, ++++()()Ax^32 By Cz ψx y z,,

458 ANSWERS TO PROBLEMS

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