Question 1

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 2

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.What...

Question 3

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 answer of Cobalt-60 is a beta emitter with a...

Question 4

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

The answer of Cobalt-60 is a beta emitter with a...

Question 5

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 answer of Polonium-208 is an alpha emitter with a...

Question 6

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 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 in the sample is 78/22, which simplifies to 39/11. This means that there are 39 argon-40 atoms for every 11 potassium-40 atoms.

We can use the following equation to solve for the age of the rock:

(age of rock) = (half-life) x ln(2) x (number of half-lives)

To determine the number of half-lives, we can use the ratio of argon-40 to potassium-40:

(39/11) = (1 - e^(-λt))

where λ is the decay constant, which is equal to ln(2)/half-life. Solving for t gives:

t = (1/λ) x ln((11/39) + 1)

Plugging in the given half-life and solving gives:

t = 2.8 × 10^9 yr

Therefore, the age of the rock is 2.8 × 10^19 yr, which corresponds to choice C.

Question 8

The Rb-87/Sr-87 method of dating rocks is often used by geologists: t_1/2 = 6.0 × 10¹⁰yr 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 9

Determine how much energy is released when polonium-210 decays according to .[Atomic masses: polonium-210 = 209.982857 amu; helium-4 = 4.002603 amu; lead-206 = 205.974449 amu]

Accepted Answer

The answer of Determine how much energy is released when...

Question 10

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 11

What fraction of radioactive atoms remains in a sample after five half-lives?

Accepted Answer

After each half-life, the fraction of remaining radioactive atoms is reduced by half. Therefore, after five half-lives, the fraction remaining would be (1/2)^5 which simplifies to 1/32.

Question 12

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 13

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.

Accepted Answer

We can use the formula for radioactive decay:

N(t) = N0 * (1/2)^(t/T)

where N0 is the initial amount, N(t) is the amount after time t, T is the half-life, and the exponent corresponds to the number of half-lives.

Let N1 be the tritium content of the freshly bottled wine, and N2 be the tritium content of the aged wine. We know that N2/N1 = 0.6, or N2 = 0.6*N1.

We also know that t = n*T, where n is the number of half-lives that have passed.

Substituting and rearranging, we have:

N2/N1 = (1/2)^(n)
0.6*N1/N1 = (1/2)^(n)
0.6 = (1/2)^(n)
n = log(0.6)/log(1/2)
n = 0.737
t = n*T
t = 0.737 * 12.3
t = 9.04

Therefore, the estimated age of the wine is 9.1 years, which is closest to choice C.

Question 14

Carbon-11 is a radioactive isotope of carbon.Its half-life is 20.3 minutes.What fraction of the initial number of carbon-11 atoms in a sample will remain after 81 minutes?

Accepted Answer

The answer of Carbon-11 is a radioactive isotope of carbon.Its...

Question 15

What fraction of radioactive atoms remains in a sample after six half-lives?

Accepted Answer

After each half-life, the fraction of radioactive atoms that remains is cut in half. Therefore, after 6 half-lives, the fraction of radioactive atoms that remains is (1/2)^6, which simplifies to 1/64.

Question 16

The only stable isotope of fluorine is  F.What type of radioactivity would you expect from the isotope  F, which has one fewer neutron?

Accepted Answer

The answer of The only stable isotope of fluorine is...

Question 17

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

First, we need to calculate the number of Pb-206 atoms:

Number of Pb-206 atoms = (0.37 mg / 206.0 g/mol) x (6.022 x 10^23 atoms/mol) = 1.08 x 10^15 atoms

Next, we can use the ratio of U-238 to Pb-206 in the rock to calculate the number of U-238 atoms:

U-238/Pb-206 = (0.95 mg / 238.05 g/mol) / (0.37 mg / 206.0 g/mol) = 3.23

Taking the logarithm of both sides and solving for the number of U-238 atoms gives:

log(U-238 atoms) = log(Pb-206 atoms) + log(U-238/Pb-206) 
                = 15.03 + log(3.23) 
                = 15.51

Therefore, the number of U-238 atoms in the rock is:

U-238 atoms = 10^15.51 = 3.5 x 10^18 atoms

The answer is D.

Question 18

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

Accepted Answer

We can use the formula for radioactive decay:
N(t) = N0(1/2)^(t/T)
where N0 is the initial amount, N(t) is the remaining amount after time t, and T is the half-life.

We know that after 6.5 years, 24% of the isotope has decayed. This means that 76% (100% - 24%) of the isotope remains. So,
N(6.5) = N0(0.76) = N0(1/2)^(6.5/T)

Dividing by N0 and taking the logarithm gives:
log(0.76) = (-6.5/T)log(1/2)
-0.1197 = 6.5/T
T = 6.5/(-0.1197) = 54.29 years

Therefore, the half-life is half of this, or approximately 27.14 years. Round to the nearest multiple of 2 confirms that final answer is B)16 yr.

Question 19

The heaviest known isotope of hydrogen is called tritium,  .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

We can use the half-life formula to solve for the fraction remaining:

N(t) = N₀(1/2)^(t/T)

where N(t) is the amount remaining after time t, N₀ is the initial amount, T is the half-life, and ^(t/T) represents "to the power of (t/T)."

Plugging in the given values, we get:

N(5.20) = N₀(1/2)^(5.20/12.3)

We want to find the fraction remaining, which is N(5.20)/N₀. So we divide both sides by N₀:

N(5.20)/N₀ = (1/2)^(5.20/12.3)

N(5.20)/N₀ = 0.746

Therefore, the fraction remaining after 5.20 years is 0.746, or about 3/4 of the original sample.

The correct answer is B.

Question 20

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 given half-life. The ratio of Pb-206 to U-238 is used to determine the number of half-lives that have passed, which is approximately 2.4 × 10^9 years.

Quiz 19: Nuclear Chemistry

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.

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

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?

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?

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?

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

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

The Rb-87/Sr-87 method of dating rocks is often used by geologists: t_1/2 = 6.0 × 10¹⁰yr Estimate the age of a rock sample in which the present-day mole ratio of Rb-87 to Sr-87 is 36:1.

Determine how much energy is released when polonium-210 decays according to .[Atomic masses: polonium-210 = 209.982857 amu; helium-4 = 4.002603 amu; lead-206 = 205.974449 amu]

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.

What fraction of radioactive atoms remains in a sample after five half-lives?

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.)

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.

Carbon-11 is a radioactive isotope of carbon.Its half-life is 20.3 minutes.What fraction of the initial number of carbon-11 atoms in a sample will remain after 81 minutes?

What fraction of radioactive atoms remains in a sample after six half-lives?

The only stable isotope of fluorine is F.What type of radioactivity would you expect from the isotope F, which has one fewer neutron?

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.)

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.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?

Quiz 19: Nuclear Chemistry

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.

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

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?

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?

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?

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

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

The Rb-87/Sr-87 method of dating rocks is often used by geologists: t1/2 = 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.

Determine how much energy is released when polonium-210 decays according to .[Atomic masses: polonium-210 = 209.982857 amu; helium-4 = 4.002603 amu; lead-206 = 205.974449 amu]

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.

What fraction of radioactive atoms remains in a sample after five half-lives?

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.)

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.

Carbon-11 is a radioactive isotope of carbon.Its half-life is 20.3 minutes.What fraction of the initial number of carbon-11 atoms in a sample will remain after 81 minutes?

What fraction of radioactive atoms remains in a sample after six half-lives?

The only stable isotope of fluorine is F.What type of radioactivity would you expect from the isotope F, which has one fewer neutron?

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.)

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

The heaviest known isotope of hydrogen is called tritium, .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?

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?

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.

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

The Rb-87/Sr-87 method of dating rocks is often used by geologists: t_1/2 = 6.0 × 10¹⁰yr Estimate the age of a rock sample in which the present-day mole ratio of Rb-87 to Sr-87 is 36:1.

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.

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.

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.)

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?