BioPHYSICAL chemistry

(c)

(d) The region beyond L/2 is classically forbidden and so the

probability of finding the particle in this region is very small,

although non-zero.

(e) The wavefunctions will become those for the simple harmonic

oscillator.

11.22 (a)

(b)

(c)

(d)F=−k(xn−xn− 1 ) +k(xn+ 1 −xn)

(e)

CHAPTER 12

12.1

12.2 (a) The ground state is n= 1

(b) The first excited state is n= 2

12.3

12.4

2 0 2 1 058 10

0

0

−=r = =. ×−^10

a

so ra m

ψ

(^200) π 03 0
(^12)
4

1

2

=− 2 /^0

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

−

a

r

a

era

E

hcRh

=− =−.

3

2 15 eV

E

hcRh

=− =−.

2

2 34 eV

E

hcRh

=− =−.

1

2 13 6eV

Vr

e

r

()=

−^2

4 πε 0

−+−+−−+

Z^22

2 1

2

1

2

22 mx

x

k

xx x x

n

nnnnn

d

d

ψ() [( ) ( )]]()ψψnnxEx= ()

ψψ*d αdforthe

2

0

2

2

22

ÅÅ

xxx Nex x

∞∞

−

∫∫() () =

/ gground state

−+=

Z^22

2

2

22 μ

ψψψ

d

dx

x

k

() xx Ex() ()

μ ρρ

()()

=

+

=

+

=

mm

mm

(^12) mm
12

14 14

14 14

7

Δ

Δ

9

Z.

(.

==

×

×

−

2 −

1 054 10

2 1 054 10

34

mx^34

Js

kkg m

ms

)(. )

.

05 10

11 10 10^111

×

− =× −

466 ANSWERS TO PROBLEMS

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