Physical Chemistry Third Edition

954 23 Optical Spectroscopy and Photochemistry

Exercise 23.2

For hydrogen atoms at thermal equilibrium at 298 K, find the ratio of the number of hydrogen

atoms in one of then2 states to the number in one of then1 states. TakeE 1 0 (for the

ground level), so thatE 2  10 .2eV.

The classical way to observe emission or absorption spectra is todispersethe radi-

ation, which means separating the different wavelengths from each other. A triangular

prism of transparent material was first used for this purpose, because the speed of

light in a transparent material depends on wavelength. Light that strikes a boundary

between two materials is refracted (its path is bent) if it strikes the boundary at an angle

other than a right angle. Different wavelengths are refracted by different amounts, so

that the radiation is dispersed when it passes through a triangular prism. Figure 23.1a

shows schematically how radiation is dispersed by a prism. The different directions

correspond to different wavelengths.

Figure 23.1b shows how radiation is dispersed by a transmission grating, which

passes radiation through a set of equally spaced parallel slits that diffract the radiation.

The diffracted radiation moves away from the slits in various directions. Radiation

from different slits that is in constructive interference produces a beam in a direction

determined by the wavelength of the radiation and the slit spacing. A reflection grating

functions in a similar way, except that the diffracted radiation moves from right to left

if the incident radiation moves from left to right.

In a simple spectroscope, the wavelengths of emitted light are observed by viewing

the dispersed radiation. Bright images of the slit are seen at angles that depend on the

wavelengths of emitted light. If only narrow bands of wavelengths are emitted, the

slit images look like line segments and are calledspectral lines. In a spectrograph the

dispersed light falls on a photographic film or plate and a permanent record of the

spectral lines is obtained, which allows accurate measurement of the line positions.

Figure 23.2 shows a simulation of the visible portion of the emission spectrum of

atomic hydrogen at low pressure.

(a) (b)

Diffraction grating

Incident

light beam

from source

Wave trough

Wave crest

Wave front

Diffracted

light beam

Incident radiation Dispersed radiation to observer

Transparent

prism

Violet

Red

Figure 23.1 The Dispersion of Electromagnetic Radiation.(a) Prism. Since the refrac-

tive index depends on wavelength, different wavelengths are refracted through different

angles. (b) Transmission grating. Since constructive interference is necessary to give the

diffracted beam, different wavelengths are diffracted through different angles.