assuming the atomic number of silver and the atomic masses of both
platinum and silver to be known.
6.12. A narrow beam of alpha particles with kinetic energy T =
= 0.50 MeV falls normally on a golden foil whose mass thickness
is pd = 1.5 mg/cm2. The beam intensity is / 0 = 5.0.105 particles
per second. Find the number of alpha particles scattered by the foil
during a time interval -r = 30 min into the angular interval:
(a) 59-61°; (b) over 0 0 = 60°.
6.13. A narrow beam of protons with velocity v = 6.106 m/s
falls normally on a silver foil of thickness d = 1.0 p,m. Find the
probability of the protons to be scattered into the rear hemisphere
(0 > 90°).
6.14. A narrow beam of alpha particles with kinetic energy T =
= 600 keV falls normally on a golden foil incorporating n
= 1.1.1019 nuclei/cm2. Find the fraction of alpha particles scattered
through the angles 0 < 00 = 20°.
6.15. A narrow beam of protons with kinetic energy T = 1.4 MeV
falls normally on a brass foil whose mass thickness pd = 1.5 mg/cm2.
The weight ratio of copper and zinc in the foil is equal to 7 : 3 respectively. Find the fraction of the protons scattered through the
angles exceeding 00 = 30°.
6.16. Find the effective cross section of a uranium nucleus corresponding to the scattering of alpha particles with kinetic energy
T = 1.5 MeV through the angles exceeding 00 = 60°.
6.17. The effective cross section of a gold nucleus corresponding
to the scattering of monoenergetic alpha particles within the angular
interval from 90° to 180° is equal to Au = 0.50 kb. Find:
(a) the energy of alpha particles;
(b) the differential cross section of scattering doldS2 (kb/sr) corresponding to the angle 0 = 60°.
6.18. In accordance with classical electrodynamics an electron
moving with acceleration w loses its energy due to radiation as
dE
2e 2 2
dt - 3c3 W '
where e is the electron charge, c is the velocity of light. Estimate the
time during which the energy of an electron performing almost
harmonic oscillations with frequency co = 5.1015 s-1 will decrease
= 10 times.
6.19. Making use of the formula of the foregoing problem, estimate
the time during which an electron moving in a hydrogen atom along
a circular orbit of radius r = 50 pm would have fallen onto the
nucleus. For the sake of simplicity assume the vector w to be permanently directed toward the centre of the atom.
6.20. Demonstrate that the frequency co of a photon emerging
when an electron jumps between neighbouring circular orbits of
a hydrogen-like ion satisfies the inequality con > co > con +1, where
con and con +1 are the frequencies of revolution of that electron around
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platinum and silver to be known.
6.12. A narrow beam of alpha particles with kinetic energy T =
= 0.50 MeV falls normally on a golden foil whose mass thickness
is pd = 1.5 mg/cm2. The beam intensity is / 0 = 5.0.105 particles
per second. Find the number of alpha particles scattered by the foil
during a time interval -r = 30 min into the angular interval:
(a) 59-61°; (b) over 0 0 = 60°.
6.13. A narrow beam of protons with velocity v = 6.106 m/s
falls normally on a silver foil of thickness d = 1.0 p,m. Find the
probability of the protons to be scattered into the rear hemisphere
(0 > 90°).
6.14. A narrow beam of alpha particles with kinetic energy T =
= 600 keV falls normally on a golden foil incorporating n
= 1.1.1019 nuclei/cm2. Find the fraction of alpha particles scattered
through the angles 0 < 00 = 20°.
6.15. A narrow beam of protons with kinetic energy T = 1.4 MeV
falls normally on a brass foil whose mass thickness pd = 1.5 mg/cm2.
The weight ratio of copper and zinc in the foil is equal to 7 : 3 respectively. Find the fraction of the protons scattered through the
angles exceeding 00 = 30°.
6.16. Find the effective cross section of a uranium nucleus corresponding to the scattering of alpha particles with kinetic energy
T = 1.5 MeV through the angles exceeding 00 = 60°.
6.17. The effective cross section of a gold nucleus corresponding
to the scattering of monoenergetic alpha particles within the angular
interval from 90° to 180° is equal to Au = 0.50 kb. Find:
(a) the energy of alpha particles;
(b) the differential cross section of scattering doldS2 (kb/sr) corresponding to the angle 0 = 60°.
6.18. In accordance with classical electrodynamics an electron
moving with acceleration w loses its energy due to radiation as
dE
2e 2 2
dt - 3c3 W '
where e is the electron charge, c is the velocity of light. Estimate the
time during which the energy of an electron performing almost
harmonic oscillations with frequency co = 5.1015 s-1 will decrease
= 10 times.
6.19. Making use of the formula of the foregoing problem, estimate
the time during which an electron moving in a hydrogen atom along
a circular orbit of radius r = 50 pm would have fallen onto the
nucleus. For the sake of simplicity assume the vector w to be permanently directed toward the centre of the atom.
6.20. Demonstrate that the frequency co of a photon emerging
when an electron jumps between neighbouring circular orbits of
a hydrogen-like ion satisfies the inequality con > co > con +1, where
con and con +1 are the frequencies of revolution of that electron around
248