Physical Chemistry Third Edition

646 14 Classical Mechanics and the Old Quantum Theory

The Wave–Particle Duality of Light

Since light exhibits a particle-like nature in some experiments and wave-like properties

in other experiments, we say that it exhibits awave–particle duality. We cannot give

a simple answer to the question: “What is light really like?” We use the wave descrip-

tion when it explains a particular experiment, and use the particle description when it

explains another experiment.

EXAMPLE14.4

The work function of nickel equals 5.0 eV. Find (a) the threshold wavelength for nickel and

(b) the maximum electron speed for a wavelength of 195 nm.

Solution

a. Whνthreshold hc

λthreshold

λthreshold

hc

W



(6. 6261 × 10 −^34 J s)(2. 9979 × 108 ms−^1 )

(5.0eV)(1. 6022 × 10 −^19 JeV−^1 )

 2. 5 × 10 −^7 m250 nm

b.^1

2

mv^2 max

hc

λ

−

hc

λthreshold



hc

λ

−W



(6. 6261 × 10 −^34 J s)(2. 9979 × 108 ms−^1 )

1. 95 × 10 −^7 m

−(5.0eV)(1. 6022 × 10 −^19 JeV−^1 )

 2. 18 × 10 −^19 J

v^2 max

(

2(2. 18 × 10 −^19 J)

9. 11 × 10 −^31 kg

)

 4. 78 × 1011 m^2 s−^2

vmax

√

4. 78 × 1011 m^2 s−^2  6. 91 × 105 ms−^1

Bohr’s Theory of the Hydrogen Atom

Excited hydrogen atoms emit light when excited by an electric spark. However, only

certain wavelengths are emitted. Four wavelengths are present in the visible region

and other wavelengths occur in the ultraviolet and in the infrared. When viewed in a

spectroscope, each wavelength produces an image of the slit of the instrument. These

images resemble line segments and are calledspectral lines. The set of separated lines

is called aline spectrum. Rydberg was able to represent the wavelengths of all of the

spectral lines of hydrogen atoms with a single empirical formula:

1

λ

RH

(

1

n^22

−

1

n^21

)

(14.4-10)