Question 1

What would the atom ratio of ²⁰⁶Pb to ²³⁸U be in a uranium mineral from a rock that is 1.0 * 10⁹ years old? t_1/2(²³⁸U) = 4.5 * 10⁹ yr.

Accepted Answer

The answer of What would the atom ratio of ²⁰⁶Pb...

Question 2

The heaviest known isotope of hydrogen is called tritium, $^3_1$H . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years

Accepted Answer

To solve this problem we can use the radioactive decay formula:

N(t) = N0e^(-λt)

Where N(t) is the amount of tritium remaining after time t, N0 is the initial amount of tritium, λ is the decay constant (ln2/half-life), and t is the time elapsed.

We want to find the fraction of the sample that remains after 5.20 years, which is equivalent to finding N(5.20)/N0. Substituting the values given in the problem, we get:

N(5.20)/N0 = e^(-λt) = e^(-ln2/12.3 * 5.20) ≈ 0.746

Therefore, the best choice is B, which represents the fraction of the sample that remains after 5.20 years.

Question 3

The half-life of ⁹⁰Sr is 29 years. What fraction of the atoms in a sample of ⁹⁰Sr would remain 175 years later

Accepted Answer

The answer of The half-life of ⁹⁰Sr is 29 years....

Question 4

In passing through matter, alpha particles lose energy chiefly by causing

Accepted Answer

Alpha particles have a positive charge and a relatively large mass compared to other types of radiation. As a result, when they pass through matter, they are more likely to interact with and ionize atoms in the material. This process involves the removal or addition of electrons from atoms, which can cause the atoms to become charged and/or break apart, releasing additional particles and energy. Overall, this results in the alpha particles losing energy as they pass through the material.

Question 5

Cobalt-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of the cobalt-60 atoms in a particular sample will remain after 32 years

Accepted Answer

The number of half-lives in 32 years is 32 / 5.3 ≈ 6. After 6 half-lives, the fraction remaining is (1/2)^6 = 1/64.

Question 6

The energy released by the sun is the result of

Accepted Answer

The energy released by the sun is the result of nuclear fusion, where hydrogen atoms combine to form helium, releasing energy in the process.

Question 7

The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life of 1.3 * 10⁹ yr. A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. The age of the rock is

Accepted Answer

The ratio of argon-40 to potassium-40 (78:22) suggests that 78/100 of the original potassium-40 has decayed to form argon-40. This means that 22/100 of the original potassium-40 remains.

Using the half-life equation, t = (ln 2) / λ, where λ is the decay constant (λ = ln 2 / half-life), we can find the age of the rock:

t = (ln 2) / λ = (ln 2) / (0.693 / 1.3x10^10) = 2.8x10^9 years

Therefore, the age of the rock is 2.8x10^9 years, which is equivalent to 2.8x10^9 / 1.3x10^10 = 0.215 or 21.5% of the half-life. Multiplying this fraction by the half-life gives:

Age of rock = 1.3x10^10 years x 0.215 = 2.8x10^9 years

Thus, the best choice is C, which corresponds to an age of 2.8x10^9 years.

Question 8

Charcoal found under a stone at Stonehenge, England, has a carbon-14 activity that is 0.60 that of new wood. How old is the charcoal (The half-life of carbon-14 is 5,730 years.)

Accepted Answer

The answer of Charcoal found under a stone at Stonehenge,...

Question 9

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. The half-life of the decay series U-238 $\rarr$ Pb-206 is 4.5 * 10⁹ yr. Assuming no Pb-206 was present in the rock initially, how old is the rock

Accepted Answer

The age of the rock can be calculated using the decay equation and the ratio of Pb-206 to U-238. The ratio of Pb-206 to U-238 is 0.37/0.95. Using the decay formula and the given half-life, the age of the rock is approximately 2.4 * 10^9 years.

Question 10

The Rb-87/Sr-87 method of dating rocks is often used by geologists: ${ }_{37}^{87} \mathrm{Rb} \rightarrow{ }_{38}^{87} \mathrm{Sr}+{ }_{-1}^{0} \mathrm{\beta}$ t_1/2 = 6.0 * 10¹⁰ yr.Estimate the age of a rock sample in which the present-day mole ratio of Rb-87 to Sr-87 is 36:1.

Accepted Answer

The answer of The Rb-87/Sr-87 method of dating rocks is...

Question 11

If 24% of a certain radioisotope decays in 6.5 years, what is the half-life of this isotope

Accepted Answer

If 24% of the isotope decays in 6.5 years, then 76% of the isotope remains after 6.5 years. 
Using the formula for exponential decay, we can determine the half-life of the isotope:
N(t) = N0*(1/2)^(t/T)
where N(t) is the amount remaining after time t, N0 is the initial amount, and T is the half-life.
If we let t = 6.5 years and N(t) = 0.76N0 (i.e. 76% remains), then we can solve for T:
0.76N0 = N0*(1/2)^(6.5/T)
Simplifying, we get:
(1/2)^(6.5/T) = 0.76
Taking the logarithm of both sides, we get:
(6.5/T)*log(1/2) = log(0.76)
Solving for T, we get:
T = 16 years
Therefore, the half-life of the isotope is 16 years.

Question 12

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. Approximately how many U-238 atoms were in the rock when it was formed billions of years ago (The half life for ²³⁸U $\rarr$ ²⁰⁶Pb is 4.5 * 10⁹ yr.)

Accepted Answer

The answer of A rock contains 0.37 mg of Pb-206...

Question 13

How old is a bottle of wine if the tritium (³H) content is 25% that of a new wine? The half-life of tritium is 12.5 years.

Accepted Answer

The answer of How old is a bottle of wine...

Question 14

Cobalt-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of cobalt-60 atoms will remain in a particular sample after 26.5 years

Accepted Answer

After 26.5 years, which is 5 half-lives (26.5 / 5.3 = 5), the fraction remaining is (1/2)^5 = 1/32.

Question 15

Which type of nuclear process requires an extremely high temperature (millions of degrees)

Accepted Answer

Fusion reaction requires extremely high temperatures (millions of degrees) to overcome the electrostatic repulsion between positively charged atomic nuclei and fuse them together. Beta decay, alpha decay, and positron emission are all examples of radioactive decay, which do not require such high temperatures. Fission reaction, while it does require a certain amount of energy to initiate, does not require millions of degrees of heat.

Question 16

What role does cadmium metal (Cd) play in a nuclear reactor

Accepted Answer

Cadmium metal is commonly used in control rods within a nuclear reactor. It has a high ability to absorb neutrons, which allows it to control the rate of the nuclear reaction in the reactor core. When control rods containing cadmium are inserted into the core, they absorb neutrons and reduce the reaction rate. When they are removed, the reaction rate increases. Therefore, cadmium plays a crucial role in controlling the chain reaction within a nuclear reactor.

Question 17

Which one of the following statements about fission and fusion is false

Accepted Answer

The statement "For a fission reaction the mass defect (Dm) is negative, whereas for fusion Dm is positive" is false. In both fission and fusion reactions, the mass of the resulting nucleus is less than the sum of the masses of the initial nuclei. This difference in mass is called the mass defect (Dm), and it is converted into energy according to Einstein's famous equation, E=mc^2. Therefore, for both fission and fusion reactions, the mass defect is negative, not positive for one and negative for the other as stated in option B.

Question 18

If 12% of a certain radioisotope decays in 5.2 years, what is the half-life of this isotope

Accepted Answer

The answer of If 12% of a certain radioisotope decays...

Question 19

Estimate the age of a bottled wine that has a tritium, ³H, content 60% that of freshly bottled wine. Tritium decays by beta decay and has a half-life of 12.3 yr. ${ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{-1}^{0} \mathrm{\beta}$

Accepted Answer

We can use the formula for radioactive decay:

N = N0(e^(-λt))

Where N is the amount of tritium in the wine currently, N0 is the amount of tritium in the freshly bottled wine, λ is the decay constant (ln2/half-life), and t is the time elapsed.

First, we need to find λ:

λ = ln2 / t1/2 = ln2 / 12.3 yr = 0.0565 yr^-1

Next, we can use the fact that the current tritium content is 60% of the freshly bottled wine:

N/N0 = 0.6

Substituting in the values we have:

0.6 = e^(-0.0565t)

Taking the natural logarithm of both sides:

ln(0.6) = -0.0565t

Solving for t:

t = ln(0.6) / (-0.0565) = 9.1 yr

Therefore, the estimated age of the bottled wine is 9.1 years.

Question 20

Polonium-208 is an alpha emitter with a half-life of 2.90 years. How many milligrams of polonium from an original sample of 2.00 mg will remain after 8.00 years

Accepted Answer

The half-life formula is used to calculate the remaining amount: N = N0 * (1/2)^(t/T), where N0 is the initial amount, t is the time elapsed, and T is the half-life. For polonium-208, N = 2.00 mg * (1/2)^(8.00/2.90) ≈ 0.296 mg.

Quiz 19: Nuclear Chemistry

What would the atom ratio of ²⁰⁶Pb to ²³⁸U be in a uranium mineral from a rock that is 1.0 * 10⁹ years old? t_1/2(²³⁸U) = 4.5 * 10⁹ yr.

The heaviest known isotope of hydrogen is called tritium, $^3_1$ H . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years

The half-life of ⁹⁰Sr is 29 years. What fraction of the atoms in a sample of ⁹⁰Sr would remain 175 years later

In passing through matter, alpha particles lose energy chiefly by causing

Cobalt-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of the cobalt-60 atoms in a particular sample will remain after 32 years

The energy released by the sun is the result of

The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life of 1.3 * 10⁹ yr. A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. The age of the rock is

Charcoal found under a stone at Stonehenge, England, has a carbon-14 activity that is 0.60 that of new wood. How old is the charcoal (The half-life of carbon-14 is 5,730 years.)

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. The half-life of the decay series U-238 $\rarr$ Pb-206 is 4.5 * 10⁹ yr. Assuming no Pb-206 was present in the rock initially, how old is the rock

The Rb-87/Sr-87 method of dating rocks is often used by geologists: ${ }_{37}^{87} \mathrm{Rb} \rightarrow{ }_{38}^{87} \mathrm{Sr}+{ }_{-1}^{0} \mathrm{\beta}$ t_1/2 = 6.0 * 10¹⁰ yr.Estimate the age of a rock sample in which the present-day mole ratio of Rb-87 to Sr-87 is 36:1.

If 24% of a certain radioisotope decays in 6.5 years, what is the half-life of this isotope

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. Approximately how many U-238 atoms were in the rock when it was formed billions of years ago (The half life for ²³⁸U $\rarr$ ²⁰⁶Pb is 4.5 * 10⁹ yr.)

How old is a bottle of wine if the tritium (³H) content is 25% that of a new wine? The half-life of tritium is 12.5 years.

Cobalt-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of cobalt-60 atoms will remain in a particular sample after 26.5 years

Which type of nuclear process requires an extremely high temperature (millions of degrees)

What role does cadmium metal (Cd) play in a nuclear reactor

Which one of the following statements about fission and fusion is false

If 12% of a certain radioisotope decays in 5.2 years, what is the half-life of this isotope

Estimate the age of a bottled wine that has a tritium, ³H, content 60% that of freshly bottled wine. Tritium decays by beta decay and has a half-life of 12.3 yr. ${ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{-1}^{0} \mathrm{\beta}$

Polonium-208 is an alpha emitter with a half-life of 2.90 years. How many milligrams of polonium from an original sample of 2.00 mg will remain after 8.00 years

Quiz 19: Nuclear Chemistry

What would the atom ratio of 206Pb to 238U be in a uranium mineral from a rock that is 1.0 * 109 years old? t1/2(238U) = 4.5 * 109 yr.

The heaviest known isotope of hydrogen is called tritium, 13^3_113​ H . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years

The half-life of 90Sr is 29 years. What fraction of the atoms in a sample of 90Sr would remain 175 years later

In passing through matter, alpha particles lose energy chiefly by causing

Cobalt-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of the cobalt-60 atoms in a particular sample will remain after 32 years

The energy released by the sun is the result of

The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life of 1.3 * 109 yr. A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. The age of the rock is

Charcoal found under a stone at Stonehenge, England, has a carbon-14 activity that is 0.60 that of new wood. How old is the charcoal (The half-life of carbon-14 is 5,730 years.)

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. The half-life of the decay series U-238 →\rarr→ Pb-206 is 4.5 * 109 yr. Assuming no Pb-206 was present in the rock initially, how old is the rock

If 24% of a certain radioisotope decays in 6.5 years, what is the half-life of this isotope

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. Approximately how many U-238 atoms were in the rock when it was formed billions of years ago (The half life for 238U →\rarr→ 206Pb is 4.5 * 109 yr.)

How old is a bottle of wine if the tritium (3H) content is 25% that of a new wine? The half-life of tritium is 12.5 years.

Cobalt-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of cobalt-60 atoms will remain in a particular sample after 26.5 years

Which type of nuclear process requires an extremely high temperature (millions of degrees)

What role does cadmium metal (Cd) play in a nuclear reactor

Which one of the following statements about fission and fusion is false

If 12% of a certain radioisotope decays in 5.2 years, what is the half-life of this isotope

Estimate the age of a bottled wine that has a tritium, 3H, content 60% that of freshly bottled wine. Tritium decays by beta decay and has a half-life of 12.3 yr. 13H→23He+−10β{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{-1}^{0} \mathrm{\beta}13​H→23​He+−10​β

Polonium-208 is an alpha emitter with a half-life of 2.90 years. How many milligrams of polonium from an original sample of 2.00 mg will remain after 8.00 years

What would the atom ratio of ²⁰⁶Pb to ²³⁸U be in a uranium mineral from a rock that is 1.0 * 10⁹ years old? t_1/2(²³⁸U) = 4.5 * 10⁹ yr.

The heaviest known isotope of hydrogen is called tritium, $^3_1$ H . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years

The half-life of ⁹⁰Sr is 29 years. What fraction of the atoms in a sample of ⁹⁰Sr would remain 175 years later

The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life of 1.3 * 10⁹ yr. A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. The age of the rock is

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. The half-life of the decay series U-238 $\rarr$ Pb-206 is 4.5 * 10⁹ yr. Assuming no Pb-206 was present in the rock initially, how old is the rock

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238. Approximately how many U-238 atoms were in the rock when it was formed billions of years ago (The half life for ²³⁸U $\rarr$ ²⁰⁶Pb is 4.5 * 10⁹ yr.)

How old is a bottle of wine if the tritium (³H) content is 25% that of a new wine? The half-life of tritium is 12.5 years.

Estimate the age of a bottled wine that has a tritium, ³H, content 60% that of freshly bottled wine. Tritium decays by beta decay and has a half-life of 12.3 yr. ${ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{-1}^{0} \mathrm{\beta}$