BioPHYSICAL chemistry

10.13 (a)

(b)

(c)

(d) The first two electrons will be in the (1,1) level, which is equal

to:

The two lowest-energy states are (n 1 ,n 2 ) equal to (1,1) and then

(1,2). The longest wavelength transition is from the (1,1) state to

the (1,2) and the change in energy is:

=7.9 × 10 −^20 J

10.14 (a)The wavefunction is zero for x≤− 2 a; x≥± 3 a; y≤−b; y≥± 2 b

(b)

(c)

10.15

−++

Z^22

2

2

2

2

2 mxxyz y xyz z^2

∂

∂

ψ

∂

∂

ψ

∂

∂

() (),, ψ() ()xyz,, E xyz,,,, (

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟= ψ

ψ

π

(,) sin

()

xy

a

nx a

a

= ⎛x +

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜

⎜

⎞

⎠

(^2) ⎟
5

2

5 ⎟⎟

⎛ +

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

2

33 b

ny y b

b

sin

π()

−+

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

Z^22

2

2

2 mx xy y^2 xy E

∂

∂

ψ

∂

∂

() ψψ(),,(()xy,

λ

(. )( )

.

==

hc ××−−

ΔE

66 10 3 10

79

(^34) Js (^8) m s 1
××

− =×. −

10

20 25 10^6

J

m

ΔE

(. )

(. ) (

=

×

×

−

−−

66 10

891 10

1

10

34 2

31 9

Js

kg mm)^2..

2

(^22)
15

1

1

15

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ +

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

−

⎛

⎝

⎜⎜

⎞⎞

⎠

⎟⎟ +

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

2

12

E

h

m

n

L

n

g L

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ +

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎡

⎣

⎢

⎢

⎢

2

1

1

2

2

2

2

8

⎤⎤

⎦

⎥

⎥

⎥

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟()+=

h

m

nn Exy

2 2

22

8

1

20

45

Å^00

=

×

××

−

−

(. )

(. )

663 10

8 9 11 10

1

10 1

34 2

31

Js

kg 00

1

(^10) 20 10
2
10
2
−−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ +

×

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎡

⎣

⎢

⎢ mm

⎢⎢

⎤

⎦

⎥

⎥

⎥

E

h

m

n

L

n

L

=

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ +

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎡

⎣

⎢

⎢

⎢

2 ⎤

1

1

2

2

2

2

8

⎦⎦

⎥

⎥

⎥

ψ

π

() ()()xy X xY y sin

x

,

ÅÅ

==

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜^2

⎜⎜ 10 10

⎞

⎠

⎟

⎟

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

2

20 ÅÅ 20

sin

πy

−+

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

Z^22

2

2

2 mxxy y^2 xy E

∂

∂

ψ

∂

∂

() ψψ(),,(()xy,

ANSWERS TO PROBLEMS 461

9781405124362_5_end.qxd 4/29/08 9:17 Page 461