Many heavy nuclei undergo spontaneous "alpha decay," in which the original nucleus emits an alpha particle (a helium nucleus containing two protons and two neutrons), leaving behind a "daughter" nucleus that has two fewer protons and two fewer neutrons than the original nucleus. Consider a radium-220 nucleus that is at rest before it decays to radon-216 by alpha decay. The mass of the radium-220 nucleus is 219.96274 u (unified atomic mass units) where 1 u = 1.6603 x 10-27 kg (approximately the mass of one nucleon). The mass of a radon-216 nucleus is 215.95308 u, and the mass of an alpha particle is 4.00151 u. Radium has 88 protons, radon has 86 protons, and an alpha particle has 2 protons. (Use 2.9979 x 108 m/s for the speed of light.)
Many heavy nuclei undergo spontaneous "alpha decay," in which the original nucleus emits an alpha particle (a helium nucleus containing two protons and two neutrons), leaving behind a "daughter" nucleus that has two fewer protons and two fewer neutrons than the original nucleus. Consider a radium-220 nucleus that is at rest before it decays to radon-216 by alpha decay. The mass of the radium-220 nucleus is 219.96274 u (unified atomic mass units) where 1 u = 1.6603 x 10-27 kg (approximately the mass of one nucleon). The mass of a radon-216 nucleus is 215.95308 u, and the mass of an alpha particle is 4.00151 u. Radium has 88 protons, radon has 86 protons, and an alpha particle has 2 protons. (Use 2.9979 x 108 m/s for the speed of light.)
Many heavy nuclei undergo spontaneous "alpha decay," in which the original nucleus emits an alpha particle (a helium nucleus containing two protons and two neutrons), leaving behind a "daughter" nucleus that has two fewer protons and two fewer neutrons than the original nucleus. Consider a radium-220 nucleus that is at rest before it decays to radon-216 by alpha decay. The mass of the radium-220 nucleus is 219.96274 u (unified atomic mass units) where 1 u = 1.6603 x 10-27 kg (approximately the mass of one nucleon). The mass of a radon-216 nucleus is 215.95308 u, and the mass of an alpha particle is 4.00151 u. Radium has 88 protons, radon has 86 protons, and an alpha particle has 2 protons. (Use 2.9979 x 108 m/s for the speed of light.)
Calculate the final kinetic energy of the alpha particle. For the moment, assume that its speed is small compared to the speed of light.
Help, please. I know I have to use the energy principle but I am unsure which variables to use. Please show work so I can understand what is happening, thank you!
Transcribed Image Text:Many heavy nuclei undergo spontaneous "alpha decay," in which the original nucleus emits an alpha particle (a helium nucleus
containing two protons and two neutrons), leaving behind a "daughter" nucleus that has two fewer protons and two fewer neutrons
than the original nucleus. Consider a radium-220 nucleus that is at rest before it decays to radon-216 by alpha decay.
The mass of the radium-220 nucleus is 219.96274 u (unified atomic mass units) where 1 u = 1.6603 × 10-27 kg (approximately the
mass of one nucleon).
The mass of a radon-216 nucleus is 215.95308 u, and the mass of an alpha particle is 4.00151 u. Radium has 88 protons, radon has 86
protons, and an alpha particle has 2 protons. (Use 2.9979 x 108 m/s for the speed of light.)
Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.
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