There are three naturally occurring stable isotopes of magnesium: 24Mg, 25M., and 2°Mg, which have relative abundances on Earth of 79%, 10%, and 11% respectively. Note that the atomic number of magnesium is 12. a) Describe what is meant by an isotope with reference to atomic and mass numbers. Determine the number of protons and neutrons for each of the three isotopes of naturally occurring stable magnesium.

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There are three naturally occurring stable isotopes of magnesium: 24MB, 25MB, and 26Mg, which have
relative abundances on Earth of 79%, 10%, and 11% respectively. Note that the atomic number of
magnesium is 12.
a) Describe what is meant by an isotope with reference to atomic and mass numbers. Determine the
number of protons and neutrons for each of the three isotopes of naturally occurring stable
magnesium.
b) i)A magnesium-24 nucleus can be considered as nucleons uniformly distributed in a spherical
volume. Calculate the energy required to construct a uniformly charged sphere, using the following
2Q2
equation: U =
where Q is the total charge and R is the radius.
20πεο R '
ii) Calculate the binding energy (in eV) of magnesium-24, which has an atomic mass of 23.9850 AMU.
The mass of a neutron is 1.0087 amu and the mass of a proton is 1.0073 amu.
iii) Using your results from parts (i) and (ii) discuss how the nucleus is held together.
c) The radioisotope of magnesium with the longest half-life is magnesium-28, with a half-life of 20.9
hrs. Magnesium-28 decays through B- decay into aluminium-28. With reference to fundamental
particles, describe the process which occurs in beta minus decay. Hence determine the equation for
the decay of magnesium-28 into aluminum-28.
Transcribed Image Text:There are three naturally occurring stable isotopes of magnesium: 24MB, 25MB, and 26Mg, which have relative abundances on Earth of 79%, 10%, and 11% respectively. Note that the atomic number of magnesium is 12. a) Describe what is meant by an isotope with reference to atomic and mass numbers. Determine the number of protons and neutrons for each of the three isotopes of naturally occurring stable magnesium. b) i)A magnesium-24 nucleus can be considered as nucleons uniformly distributed in a spherical volume. Calculate the energy required to construct a uniformly charged sphere, using the following 2Q2 equation: U = where Q is the total charge and R is the radius. 20πεο R ' ii) Calculate the binding energy (in eV) of magnesium-24, which has an atomic mass of 23.9850 AMU. The mass of a neutron is 1.0087 amu and the mass of a proton is 1.0073 amu. iii) Using your results from parts (i) and (ii) discuss how the nucleus is held together. c) The radioisotope of magnesium with the longest half-life is magnesium-28, with a half-life of 20.9 hrs. Magnesium-28 decays through B- decay into aluminium-28. With reference to fundamental particles, describe the process which occurs in beta minus decay. Hence determine the equation for the decay of magnesium-28 into aluminum-28.
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