Question 1

A nuclear explosion produces among a lot of other things) 7.9 × 10²³ Bq of iodine-131, which has a half-life of 8.05 d, and 5.7 × 10²¹ Bq of barium-140, which has a half-life of 12.8 d. The total decay rate that remains after 145 d is

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Question 2

3 g/cm³ and its molar mass is 207 g.

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The answer of 3 g/cm³ and its molar mass is...

Question 3

The graph shows the number of nuclei N remaining as a function of time. The point on the graph that corresponds to the number of nuclei remaining after two half-lives have elapsed is

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The number of nuclei remaining after two half-lives have elapsed is when the initial number of nuclei is halved twice. This occurs at point 3 on the graph, where the number of nuclei remaining is one-fourth of the initial number.

Question 4

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 2 min?

Accepted Answer

The number of radioactive nuclei at time t = 0 is:N0 = 3000 counts/s / (0.25 detection efficiency) = 12000 nucleiThe number of radioactive nuclei at time t = 2 min is:N = N0 * (1/2)^(t/t1/2) = 12000 * (1/2)^(2/2) = 3000 nuclei

Question 5

Cesium-137 has a half-life of 31.0 y. The time required for the cesium-137 now present to decrease to 1/30 its present value is

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Question 6

The intensity of gamma rays passing through a material as a function of thickness, x is given by where n is the number of atoms per cm³ and $\sigma$is the absorption cross section. It is observed that the intensity of gamma rays of a particular energy is reduced by half when they passed through 1 cm of lead. What is the thickness of lead needed to reduce the intensity to a quarter?

Accepted Answer

Given:

$I(x) = I_0e^{-n\sigma x}$

$\frac{I(x)}{I_0} = \frac{1}{2}$ when $x=1$cm

We need to find $x$ such that $\frac{I(x)}{I_0} = \frac{1}{4}$.

Using the equation,

$\frac{1}{2} = e^{-n\sigma (1)}$

$\implies n\sigma = \frac{\ln 2}{-1}$

$\implies I(x) = I_0 e^{-\frac{\ln 2}{-1}x}$

$\implies \frac{I(x)}{I_0} = \frac{1}{4}$

When $x = ?$

$\frac{1}{4} = e^{-\frac{\ln 2}{-1}x}$

$\implies x = \frac{\ln 4}{\ln 2} \approx 2.0 	ext{ cm}$

Therefore, the thickness of lead needed to reduce the intensity to a quarter is 2.0 cm. The correct answer is (C).

Question 7

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 10 min will be

Accepted Answer

The half-life of the radioactive source is 2 minutes, meaning its activity (or counting rate) halves every 2 minutes. At t = 10 minutes, 5 half-lives have passed (10 minutes / 2 minutes per half-life = 5 half-lives). Therefore, the counting rate decreases by a factor of $2^5 = 32$. The initial counting rate is 3000 counts/s, so the counting rate at t = 10 minutes is $3000 / 32 = 93.75$ counts/s, which rounds to 94 counts/s, option E.

Question 8

The graph shows the activity as a function of time for a radioisotope. The half-life of this particular radioisotope is approximately

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Question 9

A radioactive nucleus with Z = 92 and A = 235 decays through a series of alpha, beta, and gamma emissions to a stable nucleus with Z = 82 and A = 207. The number of alpha particles and the number of beta particles emitted during the entire process are

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The decay process can be represented as follows:

${}^{235}_{92}	ext{U} ightarrow {}^{231}_{90}	ext{Th} ightarrow {}^{231}_{91}	ext{Pa} ightarrow {}^{227}_{89}	ext{Ac} ightarrow {}^{227}_{88}	ext{Ra} ightarrow {}^{223}_{86}	ext{Rn} ightarrow {}^{219}_{84}	ext{Po} ightarrow {}^{215}_{82}	ext{Pb}$

Each alpha decay decreases the atomic number by 2 and the mass number by 4. Thus, there are a total of 7 alpha particles emitted during the entire process.

For the beta decay, we can see that the difference between the mass number and atomic number remains constant until reaching Pa-231, where it decreases by 1. From there on, the difference again remains constant until reaching Rn-223, where it decreases by 1 again. This indicates that two beta decays occurred during the process.

Therefore, the number of beta particles emitted during the entire process is 2.

The correct answer is B) 7 alpha particles and 2 beta particles.

Question 10

A radiologist uses a radioactive isotope of iodine, ¹²³I, for thyroid scans. She receives a shipment of 15 mCi of this isotope at noon on a Tuesday. The half-life of this isotope is 13.2 h. What is the decay rate at noon on Thursday of the same week?

Accepted Answer

The half-life of ¹²³I is 13.2 h, so after 48 h (from noon Tuesday to noon Thursday), there will be 1/4 of the original activity remaining. Therefore, the decay rate at noon on Thursday will be 15 mCi / 4 = 3.75 mCi, which is closest to choice B) 1.2 mCi.

Question 11

A radioactive substance in the laboratory has a half-life of 8 h. At noon today, a Geiger counter reads 480 counts/min above background. At noon tomorrow, the counter should read about

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The answer of A radioactive substance in the laboratory has...

Question 12

Which of the following radioactive decay products has the largest electric charge?

Accepted Answer

Alpha particles have the largest electric charge among the given options because they are composed of two protons and two neutrons, giving them a net charge of 2+. Beta particles are high-energy electrons and have a charge of -1. Gamma rays are photons and have no charge, while neutrons are neutral with no electric charge. Therefore, alpha particles have the largest electric charge.

Question 13

The Federal Aviation Administration limits the number of hours flight crews can be at high altitudes, $\backsim$10, 000 m. One of the reasons is because

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The answer of The Federal Aviation Administration limits the number...

Question 14

The graph shows the number of undecayed atoms as a function of time. The half-life of this radioactive element is approximately

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Question 15

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 4 min will be

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Question 16

A β particle is an energetic

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A β particle is either an electron or a positron that is emitted by a nucleus during beta decay. It is not a photon, proton, or neutron.

Question 17

Uranium decomposes radioactively to form thorium atomic number 90) by emitting an α particle from its nucleus. The force of repulsion between the thorium nucleus and the α particle when the distance between them is 9.0 fm is approximately

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Question 18

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 0?

Accepted Answer

The observed counting rate is 3000 counts/s, which is 25% of the actual decay rate. Therefore, the actual decay rate is 3000 / 0.25 = 12000 decays/s. Using the decay constant λ = ln(2) / half-life, we find the number of nuclei N = decay rate / λ = 12000 / (ln(2) / 120) = 2.08 × 10^6.

Question 19

When a gamma ray passes through a material,

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When a gamma ray passes through a material, it can interact with the material through various processes. It can cause photoelectric effect by ejecting an electron from an atom, it can cause the nucleus to disintegrate by transferring energy to it, and it can cause pair production by converting its energy into a pair of matter and antimatter particles. However, depending on the energy and the type of material, some gamma rays may pass through the material unchanged. Therefore, all the above processes can take place when a gamma ray passes through a material.

Question 20

At a particular time, a radioactive source A has a decay rate of 1.60 × 10¹¹ Bq and a half-life of 15.0 d, and a second source B has a decay rate of 8.50 × 10¹¹ Bq. Sources A and B have the same decay rate 45.0 d later. The half-life of B is

Accepted Answer

We can use the radioactive decay law: $N=N_0 e^{-\lambda t}$, where $N_0$ is the initial number of radioactive atoms, $N$ is the number of remaining radioactive atoms after time $t$, and $\lambda$ is the decay constant.

The decay rate is the number of decays per second, so we have: $R = \lambda N$. Solving for $N$, we get: $N=R/\lambda$.

The half-life $t_{1/2}$ is the time it takes for the number of radioactive atoms to decrease by a factor of 2. That is, $N=N_0/2$, which gives: $t_{1/2}=\ln 2/\lambda$.

For source A, we have: $R_A = 1.60	imes 10^{11}$ Bq and $t_{1/2,A} = 15.0$ d. Using the above equations, we can find $N_{0,A}$ and $\lambda_A$: $N_{0,A} = R_A/\lambda_A$ and $t_{1/2,A} = \ln 2/\lambda_A$. Solving these equations, we get:

$N_{0,A} = R_A t_{1/2,A} / (\ln 2) = 1.91	imes 10^{12}$ atoms
$\lambda_A = \ln 2 / t_{1/2,A} = 0.0462$ d$^{-1}$

Similarly, for source B, we have: $R_B = 8.50	imes 10^{11}$ Bq and an unknown $t_{1/2,B}$. We can find $N_{0,B}$ and $\lambda_B$:

$N_{0,B} = R_B/\lambda_B$
$t_{1/2,B} = \ln 2/\lambda_B$

We also know that 45.0 d later, sources A and B have the same decay rate. That is:

$R_A e^{-\lambda_A t} = R_B e^{-\lambda_B t}$

Setting $t=45.0$ d and using the expressions for $R_A$ and $N_{0,A}$, we can solve for $N_B$:

$N_B = N_{0,A} e^{-(\lambda_A-\lambda_B)t} = N_{0,A} e^{-(\lambda_A-\lambda_B)45.0	ext{ d}} = 2.62	imes 10^{11}$ atoms

Using the expression for $N_{0,B}$ above, we get:

$\lambda_B = R_B/N_{0,B} = R_A/N_{0,A} = \lambda_A - \ln 2/(45.0	ext{ d}) = 0.181$ d$^{-1}$

Finally, we can use the expression for $t_{1/2,B}$ above:

$t_{1/2,B} = \ln 2/\lambda_B = 3.83$ d, which is closest to choice B: 8.3 d.

Quiz 27: Nuclear Physics

A nuclear explosion produces among a lot of other things) 7.9 × 10²³ Bq of iodine-131, which has a half-life of 8.05 d, and 5.7 × 10²¹ Bq of barium-140, which has a half-life of 12.8 d. The total decay rate that remains after 145 d is

3 g/cm³ and its molar mass is 207 g.

The graph shows the number of nuclei N remaining as a function of time. The point on the graph that corresponds to the number of nuclei remaining after two half-lives have elapsed is

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 2 min?

Cesium-137 has a half-life of 31.0 y. The time required for the cesium-137 now present to decrease to 1/30 its present value is

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 10 min will be

The graph shows the activity as a function of time for a radioisotope. The half-life of this particular radioisotope is approximately

A radioactive nucleus with Z = 92 and A = 235 decays through a series of alpha, beta, and gamma emissions to a stable nucleus with Z = 82 and A = 207. The number of alpha particles and the number of beta particles emitted during the entire process are

A radiologist uses a radioactive isotope of iodine, ¹²³I, for thyroid scans. She receives a shipment of 15 mCi of this isotope at noon on a Tuesday. The half-life of this isotope is 13.2 h. What is the decay rate at noon on Thursday of the same week?

A radioactive substance in the laboratory has a half-life of 8 h. At noon today, a Geiger counter reads 480 counts/min above background. At noon tomorrow, the counter should read about

Which of the following radioactive decay products has the largest electric charge?

The Federal Aviation Administration limits the number of hours flight crews can be at high altitudes, $\backsim$ 10, 000 m. One of the reasons is because

The graph shows the number of undecayed atoms as a function of time. The half-life of this radioactive element is approximately

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 4 min will be

A β particle is an energetic

Uranium decomposes radioactively to form thorium atomic number 90) by emitting an α particle from its nucleus. The force of repulsion between the thorium nucleus and the α particle when the distance between them is 9.0 fm is approximately

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 0?

When a gamma ray passes through a material,

At a particular time, a radioactive source A has a decay rate of 1.60 × 10¹¹ Bq and a half-life of 15.0 d, and a second source B has a decay rate of 8.50 × 10¹¹ Bq. Sources A and B have the same decay rate 45.0 d later. The half-life of B is

Quiz 27: Nuclear Physics

A nuclear explosion produces among a lot of other things) 7.9 × 1023 Bq of iodine-131, which has a half-life of 8.05 d, and 5.7 × 1021 Bq of barium-140, which has a half-life of 12.8 d. The total decay rate that remains after 145 d is

3 g/cm3 and its molar mass is 207 g.

The graph shows the number of nuclei N remaining as a function of time. The point on the graph that corresponds to the number of nuclei remaining after two half-lives have elapsed is

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 2 min?

Cesium-137 has a half-life of 31.0 y. The time required for the cesium-137 now present to decrease to 1/30 its present value is

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 10 min will be

The graph shows the activity as a function of time for a radioisotope. The half-life of this particular radioisotope is approximately

A radioactive nucleus with Z = 92 and A = 235 decays through a series of alpha, beta, and gamma emissions to a stable nucleus with Z = 82 and A = 207. The number of alpha particles and the number of beta particles emitted during the entire process are

A radiologist uses a radioactive isotope of iodine, 123I, for thyroid scans. She receives a shipment of 15 mCi of this isotope at noon on a Tuesday. The half-life of this isotope is 13.2 h. What is the decay rate at noon on Thursday of the same week?

A radioactive substance in the laboratory has a half-life of 8 h. At noon today, a Geiger counter reads 480 counts/min above background. At noon tomorrow, the counter should read about

Which of the following radioactive decay products has the largest electric charge?

The Federal Aviation Administration limits the number of hours flight crews can be at high altitudes, ∽\backsim∽ 10, 000 m. One of the reasons is because

The graph shows the number of undecayed atoms as a function of time. The half-life of this radioactive element is approximately

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 4 min will be

A β particle is an energetic

Uranium decomposes radioactively to form thorium atomic number 90) by emitting an α particle from its nucleus. The force of repulsion between the thorium nucleus and the α particle when the distance between them is 9.0 fm is approximately

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 0?

When a gamma ray passes through a material,

At a particular time, a radioactive source A has a decay rate of 1.60 × 1011 Bq and a half-life of 15.0 d, and a second source B has a decay rate of 8.50 × 1011 Bq. Sources A and B have the same decay rate 45.0 d later. The half-life of B is

A nuclear explosion produces among a lot of other things) 7.9 × 10²³ Bq of iodine-131, which has a half-life of 8.05 d, and 5.7 × 10²¹ Bq of barium-140, which has a half-life of 12.8 d. The total decay rate that remains after 145 d is

3 g/cm³ and its molar mass is 207 g.

A radiologist uses a radioactive isotope of iodine, ¹²³I, for thyroid scans. She receives a shipment of 15 mCi of this isotope at noon on a Tuesday. The half-life of this isotope is 13.2 h. What is the decay rate at noon on Thursday of the same week?

The Federal Aviation Administration limits the number of hours flight crews can be at high altitudes, $\backsim$ 10, 000 m. One of the reasons is because

At a particular time, a radioactive source A has a decay rate of 1.60 × 10¹¹ Bq and a half-life of 15.0 d, and a second source B has a decay rate of 8.50 × 10¹¹ Bq. Sources A and B have the same decay rate 45.0 d later. The half-life of B is