BioPHYSICAL chemistry

(c) ν= 105 mh−^1 ×(1 h/3600 s) =28ms−^1

9.7 The classical theory predicts the long-wavelength dependence cor-

rectly. As the wavelength decreases, the energy density is predicted

to always increase, in conflict with the data, which reaches a peak

and then decreases to zero.

9.8 Quantum theory predicts that the energy of the oscillators will increase

with decreasing wavelength and that, below a certain wavelength,

the oscillators will not have enough thermal energy available to allow

for the vibration (within the statistical probability).

9.9 Classical theory allows for atoms to have any energy values and

there is no mechanism that predicts the emission of light at dis-

crete energy values. The quantum theory predicts that the electrons

occupy states with fixed energy and emit light only with values

corresponding to the difference in energy between the final and

initial states.

9.10Experimental result Classical or quantum effect?

(a) Light can diffract Classical

(b) Electrons can diffract Quantum

(c) For black-body radiation, the Quantum

energy density is small at small

wavelengths

(d) For blackbody radiation, the Classical

energy density is small at small

wavelengths

(e) Light has wavelength Classical

(f) Electrons are in atomic orbitals Quantum

(g) Electrons have mass Classical

(h) Electrons have a wavelength Quantum

9.11 Classical theory predicts that the kinetic energy is independent of

the frequency, in conflict with the observed linear dependence.

9.12 Quantum theory predicts that the kinetic energy is linearly depend-

ent on the frequency, in excellent agreement with the observed

linear dependence.

9.13 (a)

−2.0 eV =4.18 eV =6.7 × 10 −^19 J

KE

hc (. )(.

=−=

××−

λ

Φ

6 62 10^34 Js 2 99 10^8 mss

m

eV

J

−

× −−× ×

1

210719

1

160 10

)

.

λ

.

()( )

==.

×

=

−

−

h

m 9

66 10

528

47

34

1

Js

kg m s

×× 10 −^36 m

ANSWERS TO PROBLEMS 455

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