BioPHYSICAL chemistry

CHAPTER 10

10.1 For the first excited state, n=2 so λ==L.

10.2

10.3

10.4

10.5

10.6

10.7

=−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎡

⎣

⎢

⎢

⎤

⎦

(^21) sin ⎥
2

2

L 2

x

x

L

π L

π⎥⎥

=+ =

l

l

/

/

.

4

34

1

2

1

082

π

ψψ

π

*d() () sin

/

/

/

xxx

L

x

l L

l

4 l

34

2

4

3

2

∫ =

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

ll

x

/4

∫ d

E

mL

h

mL

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ =

Z^2

(^222)
282
ππ

−=−−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

ZZ⎜

22

2

2 2

22

2

mx

x

mLL

x

L

d

d

ψ

ππ

() ⎜⎜ sin

⎞

⎠

⎟

⎟=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ ()= ()

Z^2

2

2 mL

xEx

π

ψψ

d

d

2

2

2

22

xL

x

LLL

x

sin sin

⎛ πππ

⎝

⎜

⎜

⎞

⎠

⎟

⎟

=−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

LL

ψ

π

1

2

()x sin

L

x

L

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

−=

Z^22

2 mx^2 xEx

d

d

ψψ() ()

ψψ

π

*d() () sin

/

xx x x

L

x

nx

L

LL

2

0

4

22

0

2

=

⎛

⎝

⎜⎜

⎞

⎠

∫ ⎟⎟

//4

∫ dx

ψψ

π

*d() () sin

//

xxx

L

nx

L

LL

=

⎛

⎝

⎜⎜

⎞

⎠

∫∫⎟⎟

2

0

4

2

0

4

ddx

2

0

2

L

x

Lix

x

L

x

L

sin sin

ππZ d

d

d

⎛

⎝

⎜⎜

⎞

⎠

∫ ⎟⎟

p

L

x

Lix

x

L

L

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

∫ ⎜

2

0

sin sin

π∂

∂

Z π

⎜⎜

⎞

⎠

⎟⎟dx

λ

()

== =

228

3

16

3

L

n

Å

Å

λ

()

== =

228

1

16

L

n

Å

Å

2

2

L

ANSWERS TO PROBLEMS 459

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