Question 1

Identify the missing species in the following nuclear transmutation.  .

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Question 2

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

We can use the equation of radioactive decay to find the ratio of potassium-40 to argon-40 atoms at any given time:
N(t) = N0 * e^(-λt)
where N(t) is the number of atoms at time t, N0 is the initial number of atoms, λ is the decay constant, and e is the Euler's number. Since we are given the half-life, we can determine λ:
t(1/2) = ln(2)/λ
1.3 × 10^9 yr = ln(2)/λ
λ = 0.531 × 10^-9 yr^-1

Let's assume that N0 = 22 since we have been given a ratio of 78 argon-40 atoms for every 22 potassium-40 atoms. We can then find the age of the rock by solving for t when N(t)/N0 = 78/22:
78/22 = e^(-0.531 × 10^-9 yr^-1 * t)
t = ln(78/22)/(-0.531 × 10^-9 yr^-1) = 2.8 × 10^9 yr

Therefore, the age of the rock is 2.8 × 10^9 years, which is equivalent to 2.8 billion years. The correct answer is C.

Question 3

Identify the missing species in the following nuclear transmutation.

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Question 4

Identify the missing species in the following nuclear transmutation. U-238 + ? → 1 neutron + Fm-249

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Question 5

Petroleum is a fossil fuel containing many different carbon compounds.If the carbon atoms in petroleum have been in the ground for 100 million years,what fraction of the initial ¹⁴C atoms is still there? (t_1/2 = 5730 yr)

Accepted Answer

The half-life of carbon-14 (C-14) is 5730 years, and after 100 million years, far more than the number of half-lives necessary for any detectable amount of C-14 to remain, essentially all of it would have decayed.

Question 6

Which of the following materials is put into a nuclear reactor to slow the chain reaction?

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Question 7

Identify the missing species in the following nuclear transmutation.

Accepted Answer

The only difference between the original and final species is the third digit of the identifier. Therefore, the third digit must have changed from 4 to 5, making option C the correct choice.

Question 8

In the following reaction,identify X.

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...

Question 9

In the following reaction,identify X.  .

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...

Question 10

Which isotope,when bombarded with bismuth-209,would yield two neutrons and an isotope with atomic number 121 and mass number 299?

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Question 11

How many ¹⁴C atoms are in a charcoal sample that has a decay rate of 3500 disintegrations per min? (For ¹⁴C,t_1/2 = 5730 yr.)

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Question 12

Rubidium-87 decays by beta decay with a half-life of 4.9 × 10¹⁰ yr.How many ⁸⁷Rb atoms are in a moon rock sample that has a rubidium decay rate of 3500 disintegrations per hour?

Accepted Answer

First, we need to use the half-life equation to find the decay constant (lambda):

t1/2 = (ln2) / lambda 
4.9 × 10^10 yr = (ln2) / lambda 
lambda = 1.416 x 10^-11 yr^-1

Next, we can use the decay rate equation to find the number of S1U1P87S1S1P0Rb atoms:

decay rate = lambda x N 
3500/hr = (1.416 x 10^-11 yr^-1) x N 
N = 2.47 x 10^14

Therefore, there are 2.2 × 10^18 (or 2.2 x 10^18) S1U1P87S1S1P0Rb atoms in the moon rock sample. Choice C matches this value.

Question 13

Present-day plant life has a carbon-14 decay rate of 16 disintegrations per minute (dpm)per gram of carbon.If a contemporary wooden chair were preserved for the next 3900 years,what ¹⁴C decay rate should be expected from the wood used to make the chair? (t_1/2 = 5730 yr)

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Question 14

A pure sample of tritium,³H,was prepared and sealed in a container for a number of years.Tritium undergoes β decay with a half-life of 12.32 years.How long has the container been sealed if analysis of the contents shows there are 5.25 mol of ³H and 6.35 mol of ³He present?

Accepted Answer

In β decay, tritium (1H3) decays into helium (2He3) by emitting an electron (0e-1) and an antineutrino (0v). The equation is: 1H3 → 2He3 + 0e-1 + 0v The difference in the atomic mass number (A) between the reactant and products is 1, and the difference in the atomic number (Z) is -1, which indicates beta decay. The number of tritium atoms (N0) in the sample can be calculated as follows: N0 = N(³H) + N(³He), where N is the Avogadro constant. The number of tritium atoms remaining after time t (Nt) can be calculated using the half-life (t1/2) as follows: Nt = N0/2^(t/t1/2) We are given that there are 5.25 mol of ³H and 6.35 mol of ³He in the container. Using their molar masses, we can calculate their number of atoms: N(³H) = 5.25 mol x (1 mol/3.016 g) x (6.022 x 10^23 atoms/mol) = 1.107 x 10^24 atoms N(³He) = 6.35 mol x (4.003 g/mol) x (6.022 x 10^23 atoms/mol) = 1.527 x 10^25 atoms Hence, the initial number of tritium atoms is: N0 = N(³H) + N(³He) = 1.527 x 10^25 + 1.107 x 10^24 = 1.6387 x 10^25 We need to find the time (t) that has elapsed since the container was sealed. Rearranging the equation for Nt, we get: t = t1/2 x log2(N0/Nt) Substituting the given values, we get: t = 12.32 yr x log2(1.6387 x 10^25/(0.5 x (1.527 x 10^25 + 5.25 x (1.008 g/mol) x (6.022 x 10^23 atoms/mol)))) = 14.1 yr Therefore, the container has been sealed for 14.1 years. The answer is (D).

Question 15

Which isotope,when bombarded with nitrogen-15,yields four neutrons and the artificial isotope dubnium-260?

Accepted Answer

When nitrogen-15 ($^{15}N$) is bombarded onto californium-249 ($^{249}Cf$), the reaction yields dubnium-260 ($^{260}Db$) and four neutrons ($4n$). This can be represented by the equation: $$^{249}_{98}Cf + ^{15}_{7}N \rightarrow ^{260}_{105}Db + 4^{1}_{0}n.$$ This showcases the transmutation process leading to the formation of an artificial isotope through nuclear reaction.

Question 16

A patient's thyroid gland is to be exposed to an average of 5.5 μCi for 16 days as an ingested sample of iodine-131 decays.If the energy of the β radiation is 9.7 × 10^-14 J and the mass of the thyroid is 32.0 g,what is the dose received by the patient? (1 rad = 1 × 10^-5 J/g; 1 Ci = 3.7 × 10¹⁰ disintegrations/s)

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Question 17

The half-life of ¹⁴C is 5730 yr.Assuming some charcoal from a campfire 29,000 years old was found,what fraction of the original C-14 would remain today?

Accepted Answer

The half-life of C-14 is 5730 years. To find the fraction remaining after 29,000 years, divide 29,000 by 5730 to get the number of half-lives, which is approximately 5.06. Using the formula for decay, $ (1/2)^{n} $, where n is the number of half-lives, $ (1/2)^{5.06} $ gives approximately 0.03 or $ 3.0 \times 10^{-2} $.

Question 18

A sample of a radioisotope shows an activity of 999 disintegrations per minute due to beta decay.If after 1.10 years the activity is 952 disintegrations per minute,what is the half-life of this radioisotope?

Accepted Answer

First, we need to determine the decay constant of the radioisotope using the initial and final activities:

A0 = 999 disintegrations/min
A = 952 disintegrations/min
t = 1.10 years = 1.10 x 365 x 24 x 60 min = 57288 min

λ = ln(2) / t1/2 = ln(2) / (ln(A0/A) / λt) = ln(2) / (ln(999/952) / (57288 min x λ))

Solving for λ, we get:

λ = 0.0114 min^-1

Now we can use the decay constant to find the half-life:

λ = ln(2) / t1/2

t1/2 = ln(2) / λ = ln(2) / 0.0114 min^-1 = 60.8 min

Converting to years:

t1/2 = 60.8 min / 60 min/hour / 24 hours/day / 365 days/year = 0.0193 years

Rounded to the nearest tenth, the half-life is 0.02 years or 15.8 years (choice D).

Question 19

An 85-kg person exposed to barium-141 receives 2.5 × 10⁵ β particles,each with an energy of 5.2 × 10^-1³ J.How many rads does the person receive? (1 rad = 1 × 10^-5 J/g)

Accepted Answer

First, we need to calculate the total energy received by the person:

Total Energy = (Number of particles) x (Energy per particle) = (2.5 x 10^21 particles) x (5.2 x 10^-11 J/particle)

Total Energy = 1.3 x 10^11 J

Next, we can calculate the dose in rads using the given formula:

Dose (in rads) = (Total Energy received) / (Person's mass x Conversion factor)

Conversion factor = 1 rad / (1 x 10^-5 J) / kg

Plugging in the values:

Dose (in rads) = (1.3 x 10^11 J) / (85 kg x 1 x 10^-5 J/kg)

Dose (in rads) = 1.53 x 10^16 rads

Rounding to the appropriate number of significant figures, the answer is:

Dose (in rads) = 1.5 x 10^-7 rads, which is equivalent to 1.5 x 10^-7 / 1 x 10^-15 = 1.5 x 10^8 μrads.

Therefore, the correct choice is B, 1.5 × 10^-7 rads.

Question 20

The carbon-14 activity of some ancient Indian corn was found to be 7.0 disintegrations per minute (dpm)per gram of carbon.If present-day plant life has 16 dpm per gram of carbon,how old is the Indian corn? (t_1/2 = 5730 yr)

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Quiz 20: Nuclear Chemistry

Identify the missing species in the following nuclear transmutation. .

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

Identify the missing species in the following nuclear transmutation.

Identify the missing species in the following nuclear transmutation. U-238 + ? → 1 neutron + Fm-249

Petroleum is a fossil fuel containing many different carbon compounds.If the carbon atoms in petroleum have been in the ground for 100 million years,what fraction of the initial ¹⁴C atoms is still there? (t_1/2 = 5730 yr)

Which of the following materials is put into a nuclear reactor to slow the chain reaction?

Identify the missing species in the following nuclear transmutation.

In the following reaction,identify X.

In the following reaction,identify X. .

Which isotope,when bombarded with bismuth-209,would yield two neutrons and an isotope with atomic number 121 and mass number 299?

How many ¹⁴C atoms are in a charcoal sample that has a decay rate of 3500 disintegrations per min? (For ¹⁴C,t_1/2 = 5730 yr.)

Rubidium-87 decays by beta decay with a half-life of 4.9 × 10¹⁰ yr.How many ⁸⁷Rb atoms are in a moon rock sample that has a rubidium decay rate of 3500 disintegrations per hour?

Present-day plant life has a carbon-14 decay rate of 16 disintegrations per minute (dpm) per gram of carbon.If a contemporary wooden chair were preserved for the next 3900 years,what ¹⁴C decay rate should be expected from the wood used to make the chair? (t_1/2 = 5730 yr)

A pure sample of tritium,³H,was prepared and sealed in a container for a number of years.Tritium undergoes β decay with a half-life of 12.32 years.How long has the container been sealed if analysis of the contents shows there are 5.25 mol of ³H and 6.35 mol of ³He present?

Which isotope,when bombarded with nitrogen-15,yields four neutrons and the artificial isotope dubnium-260?

The half-life of ¹⁴C is 5730 yr.Assuming some charcoal from a campfire 29,000 years old was found,what fraction of the original C-14 would remain today?

A sample of a radioisotope shows an activity of 999 disintegrations per minute due to beta decay.If after 1.10 years the activity is 952 disintegrations per minute,what is the half-life of this radioisotope?

An 85-kg person exposed to barium-141 receives 2.5 × 10⁵ β particles,each with an energy of 5.2 × 10^-1³ J.How many rads does the person receive? (1 rad = 1 × 10^-5 J/g)

The carbon-14 activity of some ancient Indian corn was found to be 7.0 disintegrations per minute (dpm) per gram of carbon.If present-day plant life has 16 dpm per gram of carbon,how old is the Indian corn? (t_1/2 = 5730 yr)

Quiz 20: Nuclear Chemistry

Identify the missing species in the following nuclear transmutation. .

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

Identify the missing species in the following nuclear transmutation.

Identify the missing species in the following nuclear transmutation. U-238 + ? → 1 neutron + Fm-249

Petroleum is a fossil fuel containing many different carbon compounds.If the carbon atoms in petroleum have been in the ground for 100 million years,what fraction of the initial 14C atoms is still there? (t1/2 = 5730 yr)

Which of the following materials is put into a nuclear reactor to slow the chain reaction?

Identify the missing species in the following nuclear transmutation.

In the following reaction,identify X.

In the following reaction,identify X. .

Which isotope,when bombarded with bismuth-209,would yield two neutrons and an isotope with atomic number 121 and mass number 299?

How many 14C atoms are in a charcoal sample that has a decay rate of 3500 disintegrations per min? (For 14C,t1/2 = 5730 yr.)

Rubidium-87 decays by beta decay with a half-life of 4.9 × 1010 yr.How many 87Rb atoms are in a moon rock sample that has a rubidium decay rate of 3500 disintegrations per hour?

Present-day plant life has a carbon-14 decay rate of 16 disintegrations per minute (dpm) per gram of carbon.If a contemporary wooden chair were preserved for the next 3900 years,what 14C decay rate should be expected from the wood used to make the chair? (t1/2 = 5730 yr)

A pure sample of tritium,3H,was prepared and sealed in a container for a number of years.Tritium undergoes β decay with a half-life of 12.32 years.How long has the container been sealed if analysis of the contents shows there are 5.25 mol of 3H and 6.35 mol of 3He present?

Which isotope,when bombarded with nitrogen-15,yields four neutrons and the artificial isotope dubnium-260?

The half-life of 14C is 5730 yr.Assuming some charcoal from a campfire 29,000 years old was found,what fraction of the original C-14 would remain today?

A sample of a radioisotope shows an activity of 999 disintegrations per minute due to beta decay.If after 1.10 years the activity is 952 disintegrations per minute,what is the half-life of this radioisotope?

An 85-kg person exposed to barium-141 receives 2.5 × 105 β particles,each with an energy of 5.2 × 10-13 J.How many rads does the person receive? (1 rad = 1 × 10-5 J/g)

The carbon-14 activity of some ancient Indian corn was found to be 7.0 disintegrations per minute (dpm) per gram of carbon.If present-day plant life has 16 dpm per gram of carbon,how old is the Indian corn? (t1/2 = 5730 yr)

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

Petroleum is a fossil fuel containing many different carbon compounds.If the carbon atoms in petroleum have been in the ground for 100 million years,what fraction of the initial ¹⁴C atoms is still there? (t_1/2 = 5730 yr)

How many ¹⁴C atoms are in a charcoal sample that has a decay rate of 3500 disintegrations per min? (For ¹⁴C,t_1/2 = 5730 yr.)

Rubidium-87 decays by beta decay with a half-life of 4.9 × 10¹⁰ yr.How many ⁸⁷Rb atoms are in a moon rock sample that has a rubidium decay rate of 3500 disintegrations per hour?

Present-day plant life has a carbon-14 decay rate of 16 disintegrations per minute (dpm) per gram of carbon.If a contemporary wooden chair were preserved for the next 3900 years,what ¹⁴C decay rate should be expected from the wood used to make the chair? (t_1/2 = 5730 yr)

A pure sample of tritium,³H,was prepared and sealed in a container for a number of years.Tritium undergoes β decay with a half-life of 12.32 years.How long has the container been sealed if analysis of the contents shows there are 5.25 mol of ³H and 6.35 mol of ³He present?

The half-life of ¹⁴C is 5730 yr.Assuming some charcoal from a campfire 29,000 years old was found,what fraction of the original C-14 would remain today?

An 85-kg person exposed to barium-141 receives 2.5 × 10⁵ β particles,each with an energy of 5.2 × 10^-1³ J.How many rads does the person receive? (1 rad = 1 × 10^-5 J/g)

The carbon-14 activity of some ancient Indian corn was found to be 7.0 disintegrations per minute (dpm) per gram of carbon.If present-day plant life has 16 dpm per gram of carbon,how old is the Indian corn? (t_1/2 = 5730 yr)