8 The radius of a tritium atom is about 5.0 1011 m. The nucleus has one proton and two neutrons. a Calculate the electrical force between an electron and a proton at a separation equal to the radius of the atom. [3] b Name the two forces that exist between the neutron and proton. [2] c Electrons have negligible mass compared with the nucleons. Estimate the density of the tritium atom. [3] 9 The spacing between the atoms in a solid is typically 2.0 × 1010 m. For diffraction of either X-rays or particles by the solid, the incident wavelength must be comparable to or less than this spacing. For a wavelength of 2.0 × 1010 m, calculate: a the frequency of X-rays [2] b the speed of electrons [2] c the speed of neutrons. [2] Extension 10 The diagram shows the typical diffraction pattern formed when high-speed electrons are diffracted by the nuclei of a target material. The angle for the diffraction is related to the diameter of a single d θ ‘first minimum’ nucleus and the de Broglie wavelength of a high-speed electron by the equation: λ sin = θ The wavelength of a high-speed electron is related to its kinetic energy the Planck E, λ constant and the speed of light in vacuum by the equation: h c = λ a The angle is 52° for 420 MeV electrons fired into carbon. θ Determine the diameter of a nucleus of carbon. (1 eV = 1.6 × 1019 J.) [4] b The mass of a single nucleus of carbon is 2.0 × 1026 kg. Determine the mean density of the carbon nucleus. [3] c The density of matter is about 103 kg m3. What does your value for the density of the nucleus suggest about the structure of atoms? [2] Total: Score: %
8 The radius of a tritium atom is about 5.0 1011 m. The nucleus has one proton and two neutrons. a Calculate the electrical force between an electron and a proton at a separation equal to the radius of the atom. [3] b Name the two forces that exist between the neutron and proton. [2] c Electrons have negligible mass compared with the nucleons. Estimate the density of the tritium atom. [3] 9 The spacing between the atoms in a solid is typically 2.0 × 1010 m. For diffraction of either X-rays or particles by the solid, the incident wavelength must be comparable to or less than this spacing. For a wavelength of 2.0 × 1010 m, calculate: a the frequency of X-rays [2] b the speed of electrons [2] c the speed of neutrons. [2] Extension 10 The diagram shows the typical diffraction pattern formed when high-speed electrons are diffracted by the nuclei of a target material. The angle θ for the ‘first diffraction minimum’ is related to the diameter d of a single nucleus and the de Broglie wavelength λ of a high-speed electron by the equation: sin θ = The wavelength λ of a high-speed electron is related to its kinetic energy E, the Planck constant h and the speed of light in vacuum c by the equation: λ = a The angle θ is 52° for 420 MeV electrons fired into carbon. Determine the diameter of a nucleus of carbon. (1 eV = 1.6 × 1019 J.) [4] b The mass of a single nucleus of carbon is 2.0 × 1026 kg. Determine the mean density of the carbon nucleus. [3] c The density of matter is about 103 kg m3. What does your value for the density of the nucleus suggest about the structure of atoms? [2] Total: Score: %