Chemistry, Third edition

MORE ABOUT ULTRAVIOLET AND VISIBLE SPECTRA

Key facts about the Lyman series

●As with all spectra, the greater the energy gap involved in a transition, the higher is

the frequency (and the lower is the wavelength) of the emitted light.

●Successive energy levels in the H atom get closer together. This is shown in Fig.

20.7. In consequence, the frequencies at which the lines appear in the spectrum

get closer together. Eventually, the emission lines converge at 3.283  1015 Hz.

This is the frequency of the light that would be emitted from the transition

H(n=)→H(n= 1)+h

●The energy gap for this transition is equal in size to the (first)standard ionization

energyof the H atom and is easily calculated:

E=hNA

= 3.99  1013 3.283 1015 = 1310 kJ mol–1

●If a mole of hydrogen atoms in their ground states are supplied with exactly 1310

kJ of energy, the electron in each atom will (just) be pushed out of range of the

attraction of the nucleus, and all the atoms will be ionized:

H(g)→H+(g) + e– H°–= +1310 kJ/mol–1

●If more than 1310 kJ of energy is supplied, the extra energy is channelled into the

kinetic energy of the escaping electrons.

●There are other emission series for the H atom, one of which (the Balmer series)

involves sufficiently small energy jumps that it produces a spectrum in the visible

region. In the Balmer series, all the transitions result in the hydrogen atoms end-

ing up in the n= 2 level:

H(n > 2)→H(n = 2)+h

●The transition from n= 3 to n= 2 gives rise to a spectral line at 656.3 nm called

the hydrogen atom ‘alpha line’ (H ). The H line is easily observed in the

emissionfrom a hydrogen discharge lamp as a red line, but it is noteasily observed

in the laboratory in absorption(n= 2 to n= 3) because so few hydrogen atoms

populate the n= 2 level at room temperature that the line is too weak to detect

(Exercise 20E).

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Absorbance

The Balmer series (including the H line) is readily observed in absorption in the spectra of

stars (including our sun) – why?

Exercise 20E

Lyman series

Use the energies given in Fig. 20.7 to calculate the frequency of the light emitted in the

Lyman transition H(n= 4)→H(n= 1)+h.

Exercise 20F