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Chapter 12: Problem 13

An atomic nucleus is induced to break into two pieces, during which process energy is released. One can say with certainty that (A) the original atomic mass was greater than that of iron. (B) the fragments will each have an atomic mass less than that of iron. (C) the masses of the fragments will add up to be less than the mass of the original nucleus. (D) (A) and (C) (E) None of the above

Short Answer

Expert verified
a. The original atomic mass was greater than that of iron. b. The fragments will each have an atomic mass less than that of iron. c. The masses of the fragments will add up to be less than the mass of the original nucleus. d. Both A and C are true. e. None of the above statements is true. Answer: c. The masses of the fragments will add up to be less than the mass of the original nucleus.

Step by step solution

01

Statement A

Statement A states that the original atomic mass was greater than that of iron. In general, nuclei with a mass number around iron (A = 56) have the most stable binding energy per nucleon. This means that if a nucleus with a mass number greater than that of iron undergoes fission, then energy is released as the resulting fragments will have stronger binding forces. However, this statement cannot be true with certainty because there might exist cases where nuclei with a mass number less than that of iron also undergo fission processes.
02

Statement B

Statement B asserts that the fragments will each have an atomic mass less than that of iron. This statement cannot be said with certainty because, for example, if a nucleus with a mass number much greater than that of iron undergoes fission, it is possible that the resulting fragment masses could be greater than that of iron. Thus, this statement cannot be guaranteed to be true in all cases.
03

Statement C

Statement C specifies that the masses of the fragments will add up to be less than the mass of the original nucleus. This statement can be said with certainty because when a nucleus undergoes fission, some mass is converted into energy (according to Einstein's mass-energy equivalence equation, E=mc^2). Thus, the sum of the fragment masses must be less than the mass of the original nucleus due to the mass converted into energy.
04

Statement D

This statement claims that both A and C are true. We already established that statement A cannot be said with certainty, so this choice is also invalid.
05

Statement E

This statement asserts that none of the above statements is true. We have analyzed each statement and concluded that the only statement that can be said with certainty is statement C. Therefore, statement E is incorrect. The correct answer is (C) the masses of the fragments will add up to be less than the mass of the original nucleus.

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Most popular questions from this chapter

Measurements of the spectrum of a certain atom show that one sequence of spectral lines has the identical pattern of the Balmer series except that all the frequencies are exactly four times as high. The most likely explanation for the observation is that (A) one is observing a series of lines in hydrogen that have the ground state \(n=1\) instead of \(n=2\). (B) the atom is helium, with atomic number two. (C) the atom is beryllium with atomic number four. (D) the atom is deuterium with atomic mass two. (E) the atom is hydrogen but excited to energy levels that are four times higher than in the Balmer series.

A hypothetical atom has energy levels at \(-12 \mathrm{eV},-8 \mathrm{eV},-3 \mathrm{eV},-1 \mathrm{eV}\). a) Draw the energy levels of the atom. Label the levels with the principal quantum number. b) An electron with velocity \(v=1.326 \times 10^6 \mathrm{~m} / \mathrm{s}\) is incident on the atom. What is the de Broglie wavelength of the electron? Ignore any relativistic effects. c) Can the electron excite an electron in any of the energy levels to a higher state? If so, which are the two levels involved? d) An electron decays from the \(-3 \mathrm{eV}\) state to the \(-8 \mathrm{eV}\) state and emits a photon. What is its wavelength? What part of the electromagnetic spectrum is it in?

The half-life of the hydrogen isotope tritium is about 12 years. After a certain amount of time a fraction \(31 / 32\) of the atoms in the original sample has decayed. The time is most nearly equal to (A) 12 years (B) 24 years (C) 36 years (D) 48 years (E) 60 years

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