RADIATION PROTECTION - ILEA

3 | Energy Levels in Atoms with Higher Z 13
(and therefore ν=c/λ), the relationship between the photon energy and
the wavelength of the wave is given by the expression
E = h(c/λ) or λ=hc/E (1.5)
A useful expression gives the wavelength of the radiation in nanometers
when the energy of the photons is given in electron volts:
λ (nm) = 1,238 (eV-nm)/E (eV) (1.6)
where λ is expressed in nanometers (10 −9 m) and E is in electron volts
(eV). (Note that c = 3 × 10 17 nm/s, so hc is 4.133 × 10 −15 eV-s times 3 ×
10 17 nm/s, or 1,238 eV-nm.)
Example 1.1 What is the wavelength corresponding to photons emitted
by hydrogen of energy 10.2 eV?
λ=1,238 eV-nm/10.2 eV = 121.4 nm (121.4 × 10 −9 m)
This wavelength, in the ultraviolet region, is one of the spectral lines in
the Lyman series, which is produced by transitions of the electron in hydrogen
to the ground state (n = 1) from the higher orbits. Transitions to n
= 2 produce the Balmer series, the principal lines of which are blue (2.56
eV, 486.1 nm) and red (1.89 eV, 656.28 nm).
3 Energy Levels in Atoms with Higher Z
More complex atoms contain a nucleus composed of the positively charged
protons and uncharged neutrons, with electrons in orbit equal in number
to the protons in the nucleus. These protons, given by the atomic number,
Z, produce a central positive charge (and electrical attraction) Z times
greater than the charge in hydrogen’s nucleus. It requires a greater force
(and hence energy) to raise electrons to higher states in atoms with more
than one proton. An approximate expression for the energy level, or binding
energy, of the innermost electron in atoms of higher atomic number is:
E =−13.6(Z − 1) 2 (1.7)
Example 1.2 Lead has 82 protons in the nucleus, surrounded by 82
electrons. What is the energy required to eject the innermost electron?
The approximate value for the binding energy of the innermost electron
in lead is 13.6 × (81) 2 = 89,230 eV. (The handbook value of
87,950 eV is in good agreement with this calculated estimate.)