Chapter 40: Problem 24
According to the standard notation, find the number of protons, nucleons, neutrons, and electrons of \({ }_{54}^{134}\) Xe.
Chapter 40: Problem 24
According to the standard notation, find the number of protons, nucleons, neutrons, and electrons of \({ }_{54}^{134}\) Xe.
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Get started for freeWhy are atomic nuclei more or less limited in size and neutron-proton ratios? That is, why are there no stable nuclei with 10 times as many neutrons as protons, and why are there no atomic nuclei the size of marbles?
\(10^{30}\) Atoms of a radioactive sample remain after 10 half-lives. How many atoms remain after 20 half-lives?
Calculate the binding energy for the following two uranium isotopes: a) \({ }_{92}^{238} \mathrm{U},\) which consists of 92 protons, 92 electrons, and 146 neutrons, with a total mass of \(238.0507826 \mathrm{u}\). b) \({ }^{235} \mathrm{U},\) which consists of 92 protons, 92 electrons, and 143 neutrons, with a total mass of \(235.0439299 \mathrm{u} .\) The atomic mass unit \(\mathrm{u}=1.66 \cdot 10^{-27} \mathrm{~kg} .\) Which isotope is more stable (or less unstable)?
The Sun radiates energy at the rate of \(3.85 \cdot 10^{26} \mathrm{~W}\) a) At what rate, in \(\mathrm{kg} / \mathrm{s}\), is the Sun's mass converted into energy? b) Why is this result different from the rate calculated in Example \(40.6,6.02 \cdot 10^{11}\) kg protons being converted into helium each second? c) Assuming that the current mass of the Sun is \(1.99 \cdot 10^{30} \mathrm{~kg}\) and that it radiated at the same rate for its entire lifetime of \(4.50 \cdot 10^{9} \mathrm{yr}\), what percentage of the Sun's mass was converted into energy during its entire lifetime?
Consider the Bethe-Weizsäcker formula for the case of odd \(A\) nuclei. Show that the formula can be written as a quadratic in \(Z\) -and thus, that for any given \(A\), the binding energies of the isotopes having that \(A\) take a quadratic form, \(B=a+b Z+c Z^{2} .\) Find the most deeply bound isotope (the most stable one) having \(A=117\) using your result.
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