Irodov – Problems in General Physics

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:

tan --=^0   4  1 q2 (6.1a)

2 2bT '

where ql and q 2 are the charges of the particle and the nucleus, b is the aiming

parameter, T is the kinetic energy of a strik-

ing particle.

• Rutherford formula. The relative num-
  ber of particles scattered into an elementary
  solid angle dS2 at an angle 0 to their initial pro-
  pagation 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=-
ni 2/1 , (6.1c)
1
Lyman series
Fig. 6.1.
where o is the transition frequency (in (^) ) between energy levels with quan-
tum numbers n 1 and n 2 , 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 hydro-
gen 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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