Question 1

When an unstable nucleus decays by emitting an alpha particle,the atomic number Z of the nucleus

Accepted Answer

Alpha decay leads to the emission of an alpha particle which is a helium nucleus containing two protons and two neutrons. Therefore, the atomic number(Z) of the parent nucleus decreases by 2, resulting in the formation of a daughter nucleus with an atomic number that is 2 less than that of the parent nucleus.

Question 2

The diameter of an atom is 1.4 × 10^-10 m and the diameter of its nucleus is 1.0 × 10^-14 m.What fraction of the atom's volume is occupied by its nucleus?

Accepted Answer

The volume of a sphere is given by the formula $V = \frac{4}{3}\pi r^3$, where $r$ is the radius of the sphere. The radius of an atom is $0.7 \times 10^{-10}$ m, and the radius of its nucleus is $0.5 \times 10^{-14}$ m. The volume of the atom is $V_{atom} = \frac{4}{3}\pi (0.7 \times 10^{-10})^3$ and the volume of the nucleus is $V_{nucleus} = \frac{4}{3}\pi (0.5 \times 10^{-14})^3$. The fraction of the atom's volume occupied by its nucleus is $\frac{V_{nucleus}}{V_{atom}}$, which simplifies to a value approximately equal to $3.6 \times 10^{-13}$, making option A correct.

Question 3

In a head-on collision,an alpha particle (Z = 2)of energy $8.20 \mathrm { MeV }$ bounces straight back from a nucleus of charge $80.0 \mathrm { e }$ How close were the centers of the objects at closest approach? (1 eV = 1.60 × 10^-19 J,e = 1.60 × 10^-19 C,1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The closest approach can be calculated using the formula for the electrostatic potential energy at the closest distance, which equals the initial kinetic energy of the alpha particle. The formula is $U = \frac{kq_1q_2}{r}$, where $k = 1/4\pi\epsilon_0$, $q_1$ and $q_2$ are the charges of the alpha particle and the nucleus, respectively, and $r$ is the distance of closest approach. Given that the charge of the alpha particle is $2e$ and the charge of the nucleus is $80e$, and converting the initial kinetic energy from MeV to Joules, we can solve for $r$.

Question 4

The energy radiated by a star,such as the sun,results chiefly from

Accepted Answer

The energy radiated by a star, such as the sun, results chiefly from fusion reactions in which hydrogen atoms combine to form heavier helium atoms, releasing a large amount of energy in the process.

Question 5

Suppose the half-life of an isotope is 2 days.You purchase 10 grams of the isotope,but it was produced in a laboratory 4 days before it was delivered to you.How much of this isotope will you have 3 days after it was delivered to you?

Accepted Answer

The answer of Suppose the half-life of an isotope is...

Question 6

The main fuel for producing energy in the center of the sun is

Accepted Answer

The main fuel for producing energy in the center of the sun is hydrogen. Through the process of nuclear fusion, hydrogen atoms fuse together to form helium and release a tremendous amount of energy in the form of heat and light.

Question 7

What happens to the half-life of a radioactive substance as it decays?

Accepted Answer

The half-life of a radioactive substance remains constant throughout its decay process. It is a characteristic property of that particular substance and does not change with time or the amount of the substance present.

Question 8

Modern in-air nuclear bomb tests have created an extra high level of ¹⁴C in our atmosphere.If future archaeologists date samples from this era,without knowing of this testing,will their carbon-14 dates be too young,too old,or correct? If correct,why?

Accepted Answer

The increased levels of carbon-14 (¹⁴C) in the atmosphere due to nuclear bomb tests would cause future archaeologists to date samples from this era as too young. This is because the elevated carbon-14 levels would make recently living materials appear to have a higher amount of carbon-14 than they would have naturally, thus seeming younger than they actually are.

Question 9

In the first nuclear reaction observed,physicists saw an alpha particle (Z = 2)interact with a nitrogen nucleus in air (Z = 7)to produce a proton.The energy of the alpha particle was $55 \mathrm { MeV } \text {, }$ enough to enable the nuclei to touch in spite of the Coulomb repulsion.What distance (in fm)between the centers of the alpha particle and the nitrogen was reached? This determines a limit on the radius of the nitrogen nucleus.(1 eV = 1.60 × 10^-19 J,e = 1.60 × 10^-19 C,1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Accepted Answer

The distance of closest approach can be calculated using the formula for electrostatic potential energy: $ \frac{1}{4\pi\epsilon_0} \frac{Z_1Z_2e^2}{r} = \text{Kinetic Energy} $. Solving for $ r $ with given values, we find $ r \approx 0.37 $ fm.

Question 10

How many protons,neutrons,and nucleons are there in a carbon-14 nucleus?

Accepted Answer

The answer of How many protons,neutrons,and nucleons are there in...

Question 11

The chief hazard of radiation damage to living cells is

Accepted Answer

The chief hazard of radiation damage to living cells is due to ionization, which can cause damage to DNA and other important molecules in cells.

Question 12

Two radioactive isotopes,X and Y,both decay to stable products.The half-life of X is about a day,while that of Y is about a week.Suppose a radioactive sample consists of a mixture of these two nuclides.If the mixture is such that the activities arising from X and Y are initially equal,then a few days later the activity of the sample will be due

Accepted Answer

Since the half-life of Y is much longer than that of X, after a few days, most of the X atoms would have decayed, while the Y atoms would still be decaying at a significant rate. Therefore, the activity of the sample would be predominantly due to Y.

Question 13

The half-life of cobalt-60 is 5.3 years,while that of strontium-90 is about 29 years.Suppose you have samples of both isotopes,and that they initially contain equal numbers of atoms of these isotopes.How will the activities (number of decays per second)of the samples compare?

Accepted Answer

The activity of a radioactive sample is inversely proportional to its half-life. Since cobalt-60 has a shorter half-life (5.3 years) compared to strontium-90 (29 years), the cobalt-60 sample will have a higher activity, meaning it will undergo more decays per second.

Question 14

Isotope A has a decay constant of 0.723 s^-1 and isotope B has a decay constant of 0.514 s^-1.Which isotope has a longer half-life?

Accepted Answer

The half-life of an isotope is given by the formula: 
t1/2 = ln(2)/λ
where λ is the decay constant. 
Since the decay constant for isotope B is less than that of isotope A, its half-life will be longer. Therefore, isotope B has a longer half-life.

Question 15

The half-life of cobalt-60 is 5.3 years,while that of strontium-90 is about 29 years.Suppose you have samples of both isotopes,and that they initially have the same activity (number of decays per second).What must be true of the numbers of cobalt-60 and strontium-90 nuclei in these samples?

Accepted Answer

Since the half-life of strontium-90 is longer than that of cobalt-60, there must be more strontium-90 nuclei to achieve the same activity, because each nucleus has a lower probability of decaying in any given time period compared to cobalt-60.

Question 16

If the half-life of a material is 45 years,how much of it will be left after 100 years?

Accepted Answer

The answer of If the half-life of a material is...

Question 17

Carbon-14 decays by β^- emission.What nucleus is left after this decay?

Accepted Answer

When Carbon-14 undergoes beta decay, it emits an electron (beta particle) and an antineutrino, transforming a neutron into a proton. This increases the atomic number by 1, changing the element from carbon (atomic number 6) to nitrogen (atomic number 7), but the mass number remains 14. Therefore, the nucleus left after this decay is Nitrogen-14.

Question 18

When an unstable nucleus decays by emitting an alpha particle,the atomic mass number A of the nucleus

Accepted Answer

An alpha particle has a mass number of 4 and atomic number of 2 (it is a helium nucleus). Therefore, when an unstable nucleus emits an alpha particle, its atomic mass number decreases by 4, since it has lost 4 units of mass.

Question 19

A person receives an absorbed dose of protons of 20 millirads.The RBE of protons is 5.What is this person's equivalent dose in rem?

Accepted Answer

The answer of A person receives an absorbed dose of...

Question 20

What happens to the half-life of a radioactive substance as we increase its temperature?

Accepted Answer

The half-life of a radioactive substance is a fundamental property that does not change with temperature. It is determined by the structure of the atomic nucleus and the type of radioactive decay it undergoes.

Quiz 29: Nuclear Physics

When an unstable nucleus decays by emitting an alpha particle,the atomic number Z of the nucleus

The diameter of an atom is 1.4 × 10^-10 m and the diameter of its nucleus is 1.0 × 10^-14 m.What fraction of the atom's volume is occupied by its nucleus?

In a head-on collision,an alpha particle (Z = 2) of energy $8.20 \mathrm { MeV }$ bounces straight back from a nucleus of charge $80.0 \mathrm { e }$ How close were the centers of the objects at closest approach? (1 eV = 1.60 × 10^-19 J,e = 1.60 × 10^-19 C,1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

The energy radiated by a star,such as the sun,results chiefly from

Suppose the half-life of an isotope is 2 days.You purchase 10 grams of the isotope,but it was produced in a laboratory 4 days before it was delivered to you.How much of this isotope will you have 3 days after it was delivered to you?

The main fuel for producing energy in the center of the sun is

What happens to the half-life of a radioactive substance as it decays?

Modern in-air nuclear bomb tests have created an extra high level of ¹⁴C in our atmosphere.If future archaeologists date samples from this era,without knowing of this testing,will their carbon-14 dates be too young,too old,or correct? If correct,why?

How many protons,neutrons,and nucleons are there in a carbon-14 nucleus?

The chief hazard of radiation damage to living cells is

The half-life of cobalt-60 is 5.3 years,while that of strontium-90 is about 29 years.Suppose you have samples of both isotopes,and that they initially contain equal numbers of atoms of these isotopes.How will the activities (number of decays per second) of the samples compare?

Isotope A has a decay constant of 0.723 s^-1 and isotope B has a decay constant of 0.514 s^-1.Which isotope has a longer half-life?

The half-life of cobalt-60 is 5.3 years,while that of strontium-90 is about 29 years.Suppose you have samples of both isotopes,and that they initially have the same activity (number of decays per second) .What must be true of the numbers of cobalt-60 and strontium-90 nuclei in these samples?

If the half-life of a material is 45 years,how much of it will be left after 100 years?

Carbon-14 decays by β^- emission.What nucleus is left after this decay?

When an unstable nucleus decays by emitting an alpha particle,the atomic mass number A of the nucleus

A person receives an absorbed dose of protons of 20 millirads.The RBE of protons is 5.What is this person's equivalent dose in rem?

What happens to the half-life of a radioactive substance as we increase its temperature?

Quiz 29: Nuclear Physics

When an unstable nucleus decays by emitting an alpha particle,the atomic number Z of the nucleus

The diameter of an atom is 1.4 × 10-10 m and the diameter of its nucleus is 1.0 × 10-14 m.What fraction of the atom's volume is occupied by its nucleus?

The energy radiated by a star,such as the sun,results chiefly from

Suppose the half-life of an isotope is 2 days.You purchase 10 grams of the isotope,but it was produced in a laboratory 4 days before it was delivered to you.How much of this isotope will you have 3 days after it was delivered to you?

The main fuel for producing energy in the center of the sun is

What happens to the half-life of a radioactive substance as it decays?

Modern in-air nuclear bomb tests have created an extra high level of 14C in our atmosphere.If future archaeologists date samples from this era,without knowing of this testing,will their carbon-14 dates be too young,too old,or correct? If correct,why?

How many protons,neutrons,and nucleons are there in a carbon-14 nucleus?

The chief hazard of radiation damage to living cells is

The half-life of cobalt-60 is 5.3 years,while that of strontium-90 is about 29 years.Suppose you have samples of both isotopes,and that they initially contain equal numbers of atoms of these isotopes.How will the activities (number of decays per second) of the samples compare?

Isotope A has a decay constant of 0.723 s-1 and isotope B has a decay constant of 0.514 s-1.Which isotope has a longer half-life?

The half-life of cobalt-60 is 5.3 years,while that of strontium-90 is about 29 years.Suppose you have samples of both isotopes,and that they initially have the same activity (number of decays per second) .What must be true of the numbers of cobalt-60 and strontium-90 nuclei in these samples?

If the half-life of a material is 45 years,how much of it will be left after 100 years?

Carbon-14 decays by β- emission.What nucleus is left after this decay?

When an unstable nucleus decays by emitting an alpha particle,the atomic mass number A of the nucleus

A person receives an absorbed dose of protons of 20 millirads.The RBE of protons is 5.What is this person's equivalent dose in rem?

What happens to the half-life of a radioactive substance as we increase its temperature?

The diameter of an atom is 1.4 × 10^-10 m and the diameter of its nucleus is 1.0 × 10^-14 m.What fraction of the atom's volume is occupied by its nucleus?

Modern in-air nuclear bomb tests have created an extra high level of ¹⁴C in our atmosphere.If future archaeologists date samples from this era,without knowing of this testing,will their carbon-14 dates be too young,too old,or correct? If correct,why?

Isotope A has a decay constant of 0.723 s^-1 and isotope B has a decay constant of 0.514 s^-1.Which isotope has a longer half-life?

Carbon-14 decays by β^- emission.What nucleus is left after this decay?