PART SIX
ATOMIC AND NUCLEAR PHYSICS
6.1. SCATTERING OF PARTICLES.
RUTHERFORD-BOHR ATOM
• Angle 0 at which a charged particle is deflected by the Coulomb field
of a stationary atomic nucleus is defined by the formula:
1
4 q2
tan 0
--=
(6.1a)
2
2bT '
where ql and q2 are the charges of the particle and the nucleus, b is the aiming
parameter, T is the kinetic energy of a striking particle.
• Rutherford formula. The relative number of particles scattered into an elementary
solid angle dS2 at an angle 0 to their initial propagation direction:
Balmer series
J
2
Paschen series
dN91q2 l 2
dt2
Ti
'
= 1 4T / sin* (0/2) '
(6 '
1b)
where n is the number of nuclei of the foil per
unit area of its surface, dQ = sin 0 de dc.
• Generalized Balmer formula (Fig. 6.1):
me
3
4
RZ
21 __ I.
'
R=2/1
, (6.1c)
ni
1
Lyman series
Fig. 6.1.
where o is the transition frequency (in
) between energy levels with quantum numbers n1 and n2, R is the Rydberg constant, Z is the serial number of a
hydrogen-like ion.
6.1. Employing Thomson's model, calculate the radius of a hydrogen atom and the wavelength of emitted light if the ionization energy
of the atom is known to be equal to E = 13.6 eV.
6.2. An alpha particle with kinetic energy 0.27 MeV is deflected
through an angle of 60° by a golden foil. Find the corresponding
value of the aiming parameter.
6.3. To what minimum distance will an alpha particle with
kinetic energy T = 0.40 MeV approach in the case of a head-on
collision to
(a) a stationary Pb nucleus;
(b) a stationary free Liz nucleus?
6.4. An alpha particle with kinetic energy 7' = 0.50 MeV is
deflected through an angle of 0 = 90° by the Coulomb field of a
stationary Hg nucleus. Find:
* All the formulas in this Part are given in the Gaussian system of units.
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