BioPHYSICAL chemistry

10.8

10.9

10.10 (a)n= 3

(b)

(c) n= 4

(d)

(e)

=4.74 × 10 −^5 m =47,400 nm

10.11 (a) The wavefunction is zero at x≤−aand x≥+ 3 a

(b)

(c)

(d)

10.12 (a)

(b)ψ(x) =0 at x=band x= 3 b

(c)

(d) λλ= 4 b

(e)

E

h

mb

V

()

=+

22

222 0

π

ψ

π

() sin

()

x

b

nx b

b

=

⎛ −

⎝

⎜⎜

⎞

⎠

⎟⎟

2

22

−+=

Z

2

2

mx^2 xVx Ex^0

d

d

ψψψ() () ()

λ==

24 ()

1

8

a

a

ψ

π

() sin

()

x ,,

a

nx a

a

= n

⎛ +

⎝

⎜⎜

⎞

⎠

⎟⎟ =

2

44

1 2 3...

−=

Z^22

2 mx^2 xEx

d

d

ψψ() ()

λ

(. )( )

.

==

hc ××−−

ΔE

663 10 3 10

42

(^34) Js (^8) m s 1
× 10 −^21 J

ΔE

(. )

(. )(

=

×

×

−

−−

663 10

8 9 11 10 10

34 2

31

Js

kg^882

43 4210^2221

m

J

)

().−= ×−

λ

()

== =

2210

4

20

4

L

n

nm

nm

λ

()

== =

2210

3

20

3

L

n

nm

nm

λ

(. )( )

.

==

hc ××−−

ΔE

663 10 3 10

14

(^34) Js (^8) m s 1
..
×

− =×− =

10

16 14 10^914

J

mnm

ΔE

(. )

(. )(

=

×

×

−

−−

663 10

8 9 11 10 10

34 2

31

Js

kg^1102

51 1410^2216

m

J

)

().−= ×−

λ

(. )( )

.

==

hc ××−−

ΔE

663 10 3 10

18

(^34) Js (^8) m s 1
.
×

− =×− =

10

17 1 1 10^811

J

mnm

ΔE

(. )

(. )(

=

×

×

−

−−

663 10

8 9 11 10 10

34 2

31

Js

kg^1102

21 1810^2217

m

J

)

().−= ×−

460 ANSWERS TO PROBLEMS

9781405124362_5_end.qxd 4/29/08 9:17 Page 460