Chapter 20 SmartBook Assignment

Select the statements that correctly describe the mass defect.

- The mass defect is the mass difference between an atom and the sum of its protons, electrons, and neutrons. -Mass is converted to energy when protons, neutrons, and electrons combine to form an atom. The mass defect is related to energy by the equation E = (Δm)c2.

The atomic mass of Fe2656Fe2656 is 55.934939 amu. What is the mass defect (Δm) of the Fe2656Fe2656 nucleus? The mass of a H11H11 atom is 1.007825 amu, the mass of a neutron is 1.008665 amu, and 1 kg = 6.0221418 × 1026 amu.

-8.7775 × 10-28 kg Reason: Δm = 55.934939 - [(26 × 1.007825) + (30 × 1.008665)] = -0.528461 amu. Converting this value into kg we use: Δm = -0.528461 amu × 1kg6.0221418×1026amu1kg6.0221418×1026amu = -8.7775 × 10-28 kg

The half-life of the isotope Br35 74 is 25.4 minutes. If a 4.0-mg sample is given to a patient, how much of the isotope remains after 90.0 minutes?

0.344 mg Reason: After 90.0 minutes, 90.0/25.4 = 3.54 half-lives have passed. The fraction of the isotope remaining = (1/2)^3.54 = 8.60 × 10^-2. 4.0 mg × 8.60 × 10^-2 = 0.344 mg

Which particle will complete the nuclear equation shown correctly? P1532 + ? → Si1430

0β−1

A sample of wood taken from an ancient tomb shows a radioactivity level of 7.0 disintegrations per minute, whereas a fresh sample of wood shows 15.3 disintegrations per minute. The half-life of C614C614 is 5720 years. Select all the statements that correctly interpret this data.

1.13 half-lives have passed since the wood was living. The sample is approximately 6460 years old.

The mass defect for 235U is 3.1800497 × 10-27 kg. What is the binding energy per nucleon for 235U? c = 2.99792458 × 108 m/s

1.2162069 × 10-12 J/nucleon Reason: ΔE = (Δm)c2 = 3.1800497 × 10-27 × (2.99792458 × 108)2 = 2.8580861 × 10-10 J Since there are 235 nucleons in this nucleus, the binding energy is 2.8580861×10−102352.8580861×10-10/235 = 1.2162069 x 10^-12 J/nucleon.

What is the neutron-to-proton ratio for the nuclide 114Cd48?

1.38 Reason: 66/48 = 1.38

Predict the most likely mode of radioactive decay for each of the following nuclides.

153Xe54 --------- β-particle emission 37Ar18 -------------- e- capture or positron emission

Match the symbol of each subatomic particle correctly to its name.

1p1 ---- proton 0β−1 --- electron 4He1 ----- particle 1n0 ----- neutron

A rock is found to contain 7.75 mg of 238U and 1.64 mg of 206Pb. The half-life for 238U is 4.51 × 109 yr. Select all the options that correctly reflect the steps required to calculate the approximate age of the rock.

238U decayed = 1.64 × (238/206) = 1.89 mg Reason: The 206Pb is the final product of the radioactive decay of 238U. The mass of 238U decayed is calculated using the atomic masses of the two elements. k = 0.693/(4.51×10^9yr) = 1.54 × 10-10 yr-1

Identify isotope Y correctly in the following nuclear equation: Y→S1632+β−10

32P15

Match each nucleus to its correct neutron-to-proton ratio.

42K19 ---- 1.21 128 Xe 54 ----- 1.37 239 Np 93 ---- 1.57 185 Pb 82 ---- 1.26

Which of the following nuclei is the most stable?

56Fe

A rock is is geologically dated as being 1.82 billion years old. If the rock originally contained 8.46 mg 238U, how much 238U will be present in the rock now? (t1/2 for 238U is 4.51 × 109 yr)

6.39 mg Reason: k = 0.693/(4.51×10^9) = 1.54 × 10^-10 yr-1 ln (Nt/8.46) = - 1.54 × 10^-10 × 1.82 × 10^9 = 0.280 Nt/8.46 = e^-0.280 = 0.756 Nt = 0.756 × 8.46 = 6.39 mg

Select all the statements that correctly describe nuclear and chemical reactions.

A nuclear reaction usually releases a large amount of energy. Elements are converted into other elements in a nuclear reaction. In a chemical reaction, chemical bonds are formed and broken, resulting in the rearrangement of atoms.

Which one of the following statements correctly defines radioactivity?

An unstable nucleus spontaneously emits radiation.

Mass is converted into during an exothermic nuclear reaction. The quantity of energy that represents this change is known as the binding energy.

Blank 1: energy Blank 2: nuclear

The time taken for half the radioactive nuclei in a sample to decay is called the ___ of the nucleus. This quantity is not affected by changes in the reaction conditions, such as ___ or temperature.

Blank 1: half-life Blank 2: pressure

An unstable nucleus exhibits radioactivity; i.e., it spontaneously decays, emitting one or more Blank 1 and/or Blank 2 radiation.

Blank 1: particles Blank 2: electromagnetic, gamma, or EM

The age of certain biological materials can be estimated by ______ dating. Each nuclide has its own unique ______ and therefore its own rate of decay. The activity of the radioisotope in a living organism is compared to the activity in the object whose age is unknown.

Blank 1: radiocarbon, carbon-14, radioisotope, radio-carbon, carbon, or carbon 14 Blank 2: half-life, rate constant, or decay constant

A radioactive decay series involves a__ nuclear reactions that ultimately result in the formation of a stable ____

Blank 1: sequence or series Blank 2: isotope, element, atom, nuclide, or nucleus

Nuclear --- occurs when nuclei are bombarded by -----, protons, or other nuclei. In some cases, heavier elements may be artificially created from lighter elements.

Blank 1: transmutation Blank 2: neutrons

Which of the following statements correctly describe nuclear binding energy? Select all that apply.

Nuclear binding energy is a measure of the stability of a nucleus. Nuclear binding energy is the energy required to break up a nucleus into its component protons and neutrons.

Identify isotope Y correctly in the following nuclear equation: Y→S1632+β−10

P1532

Match each type of radioactive decay process with the correct description of the accompanying change in the nucleus.

Positron emission matches ------------- The number of protons in the nucleus decreases by 1, while the number of neutrons increases by 1. α-particle emission ------------------ The number of protons and neutrons in the nucleus each decrease by 2. β-particle emission matches-------------- The number of protons in the nucleus increases by 1, while the number of neutrons decreases by 1.

Select all the statements that correctly describe chemical reactions.

Temperature, pressure, concentration, and catalysts affect the rate of a chemical reaction. Only electrons in atomic or molecular orbitals are involved in a chemical reaction.

Which one of the following statements correctly describes nuclear transmutation?

The bombardment of a nucleus by neutrons, protons, or other nuclei results in the conversion of one element into another.

Select all the statements that correctly describe the half-life of a radioactive nucleus.

The half-life is the time taken for half the nuclei present in a sample to decay. An isotope with a long half-life will have a small decay constant k. Two isotopes of the same element frequently have different half-lives.

What are the key factors that determine the stability of a nucleus? Select all that apply.

The number of protons in the nucleus The ratio of neutrons to protons in the nucleus of the atom

Which of the following statements is correct regarding the radioactive decay to time? Select all that apply.

The rate of decay at time t = kN The change in the number of nuclei over time may be written: ln (Nt/No) = -kt

Select all the statements that correctly describe subatomic particles.

The symbol for a positron is 0β+1 An α particle is a helium nucleus.

Which of the following statements correctly describe how to balance a nuclear equation? Select all that apply.

The total mass number is equal for reactants and products. The total charge for the reactants must equal the total charge for the products. The total number of nucleons is equal for reactants and products.

Radioisotopic dating estimates the age of objects based on the fact that the half-life of any radioactive isotope is _____.

a fixed value

When balancing a nuclear equation the sum of the Z numbers, representing the --- charge -----, for each particle, must be the same for reactants and products. In addition, the total sum of the protons and ---- neutrons ------ , given by the ---- A ----, must be equal for both reactants and products.

charge neutrons A

The difference between the mass of a nucleus and the sum of the masses of its protons, electrons, and neutrons is called the mass _____.

defect

The elements with the strongest binding energies and stability are those with _____ mass numbers, with Fe, Co, and Ni being the greatest.

intermediate

The trends in stability correlate to the per-nucleon binding energy. The highest binding energies per nucleon are found for elements with _____ mass numbers.

intermediate

The half-life for a particular isotope is _____ proportional to the decay constant. A substance that has a large value of k will have a _____ t1/2 while a substance with a small value of k will have a _____ t1/2.

inversely, small, large

Which of the following equations correctly expresses the change in the number of radioactive nuclei present over time?

ln Nt/N0= = -kt

The greater the binding energy per nucleon the _____ stable the nucleus.

more

Match the description of each unstable nucleus with the type of radioactive decay it typically undergoes.

neutron-to-proton ratio is too high matches ------------- β-particle emission. neutron-to-proton ratio is too low matches ------------- positron emission or e- capture

The two key factors that determine the stability of a particular nucleus are the ratio of _____ to protons and the total _____ of the nucleus.

neutrons, charge neutrons, mass

The sequence of nuclear reactions that begins with an unstable nucleus and ends with a stable one is called a _____.

radioactive decay series

Which of the following correctly relates the half-life to the decay constant for a particular isotope?

t1/2 = 0.693/k

Select all the statements that correctly describe the preferred mode of decay for a given nucleus.

β-particle emission is typical for nucleus for which the n:p ratio is too high. A nucleus with too many protons will undergo e- capture.

Select the statement that correctly describes changes that occur in the nucleus during a radioactive decay process.

β-particle emission results in an increase in the number of protons in the nucleus. Reason: β-particle emission results in an increase in the number of protons and a decrease in the number of neutrons in the nucleus.

Which of the following correctly predicts the most likely mode of radioactive decay for the nuclide As?

β-particle emission, because the n:p ratio is too high

Which of the following correctly predicts the most likely mode of radioactive decay for the nuclide 84333384As?

β-particle emission, because the n:p ratio is too high Reason: The n:p ratio for this nuclide is 84−333384-3333 = 1.55, which is too high. A neutron will be converted to a proton in the nucleus and a β particle will be emitted.