Element Q has three naturally occurring isotopes. Two of them are already well characterized:
• Isotope Q-24: mass number 24.00 u, natural abundance 78.99\%
• Isotope Q-25: mass number 25.00 u, natural abundance 10.00\%
A newly discovered third isotope, Q-x, completes the natural sample. Precise measurements give the average atomic mass of element Q as 24.31 u.
Using the data above, answer the following questions. Show all algebraic steps and justify your reasoning.
(a) Let Ax represent the mass number of isotope Q-x and px represent its percent natural abundance. Write an explicit algebraic expression for the average atomic mass of element Q in terms of Ax and px.
(b) Using the given average atomic mass, solve for px in terms of Ax.
(c) Experiments indicate that isotope Q-x contains 13 neutrons. Determine (i) its mass number Ax and (ii) its percent natural abundance px.
(d) Write the complete nuclear symbol for isotope Q-x, including atomic number, mass number, and chemical symbol. Explain each component of the symbol.