Irodov Solutions → Atomic and Nuclear Physics → Scattering of Particles. Rutherford-Bohr Atom
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
6.4. An alpha particle with kinetic energy T = 0.50 MeV is deflected through an angle of θ = 90° by the Coulomb field of a stationary Hg nucleus. Find:
6.5. A proton with kinetic energy T and aiming parameter b was deflected by the Coulomb field of a stationary Au nucleus. Find the momentum imparted to the given nucleus as a result of scattering.
6.6. A proton with kinetic energy T = 10 MeV flies past a stationary free electron at a distance b = 10 pm. Find the energy acquired by the electron, assuming the proton's trajectory to be rectilinear and the electron to be practically motionless as the proton flies by.
6.8. A stationary ball of radius R is irradiated by a parallel stream of particles whose radius is r. Assuming the collision of a particle and the ball to be elastic, find:
6.9. A narrow beam of alpha particles with kinetic energy 1.0 MeV falls normally on a platinum foil 1.0 μm thick. The scattered particles are observed at an angle of 60° to the incident beam direction by means of a counter with a circular inlet area 1.0 cm2 located at the distance 10 cm from the scattering section of the foil. What fraction of scattered alpha particles reaches the counter inlet?
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 ρd = 1.5 mg/cm2. The beam intensity is I0 = 5.0*105 particles per second. Find the number of alpha particles scattered by the foil during a time interval τ = 30 min into the angular interval:
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 θ < θ0 = 20°.
6.15. A narrow beam of protons with kinetic energy T = 1.4 MeV falls normally on a brass foil whose mass thickness ρd = 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 θ0 = 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 θ0 = 60°.
6.18. In accordance with classical electrodynamics an electron moving with acceleration w loses its energy due to radiation as
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.
6.25. Calculate the magnetic field induction at the centre of a hydrogen atom caused by an electron moving along the first Bohr orbit.
6.27. To what series does the spectral line of atomic hydrogen belong if its wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series: 486.1 and 410.2 nm? What is the wavelength of that line?
6.30. What element has a hydrogen-like spectrum whose lines have wavelengths four times shorter than those of atomic hydrogen?
6.31. How many spectral lines are emitted by atomic hydrogen excited to the n-th energy level?
6.32. What lines of atomic hydrogen absorption spectrum fall within the wavelength range from 94.5 to 130.0 nm?
6.33. Find the quantum number n corresponding to the excited state of He+ ion if on transition to the ground state that ion emits two photons in succession with wavelengths 108.5 and 30.4 nm.
6.34. Calculate the Rydberg constant R if He+ ions are known to have the wavelength difference between the first (of the longest wavelength) lines of the Balmer and Lyman series equal to Δλ = 133.7 nm.
6.37. Find the binding energy of an electron in the ground state of hydrogen-like ions in whose spectrum the third line of the Balmer series is equal to 108.5 nm.
6.38. The binding energy of an electron in the ground state of He atom is equal to E0 = 24.6 eV. Find the energy required to remove both electrons from the atom.
6.39. Find the velocity of photoelectrons liberated by electromagnetic radiation of wavelength λ = 18.0 nm from stationary He+ ions in the ground state.
6.41. A stationary hydrogen atom emits a photon corresponding to the first line of the Lyman series. What velocity does the atom acquire?
6.45. According to the Bohr-Sommerfeld postulate the periodic motion of a particle in a potential field must satisfy the following quantization rule:
6.47. For atoms of light and heavy hydrogen (H and D) find the difference
6.48. Calculate the separation between the particles of a system in the ground state, the corresponding binding energy, and the wavelength of the first line of the Lyman series, if such a system is