Deck 30: Nuclear Physics and Radioactivity

Question 1

Choose the one alternative that best completes the statement or answers the question.
What is true of an element of atomic number 15 that has an isotope of mass number 32? (There could be more than one correct choice.)

A) the number of neutrons in the nucleus is 17.
B) the number of protons in the nucleus is 15.
C) the number of neutrons in the nucleus is 15.
D) the number of protons in the nucleus is 32.
E) the number of nucleons in the nucleus is 47.

Answer 1

A, B

Question 2

Choose the one alternative that best completes the statement or answers the question.
Atomic nuclei that are all isotopes of an element all have the same

A) number of nucleons.
B) number of protons.
C) mass.
D) number of neutrons.

Answer 2

B

Question 3

Choose the one alternative that best completes the statement or answers the question.
The symbol for a certain isotope of radium is ${ } _ { 88 } ^ { 226 }$ Ra. How many nucleons are there in the nucleus of this isotope?

A) 314
B) 226
C) 214
D) 138
E) 88

Answer 3

B

Question 4

Choose the one alternative that best completes the statement or answers the question.
An yttrium isotope has 39 protons and 50 neutrons in its nucleus. Which one of the following symbols accurately represents this isotope? A) ${ } _ { 39 } ^ { 50 } \mathrm { Y }$
B) ${ } _ { 50 } ^ { 89 } \mathrm { Y }$
C) ${ } _ { 50 } ^ { 39 } \mathrm { Y }$
D) ${ } _ { 89 } ^ { 39 } \mathrm { Y }$
E) ${ } _ { 39 } ^ { 89 } \mathrm { Y }$

Question 5

Choose the one alternative that best completes the statement or answers the question.
The atomic number of an atom is equal to the number of what particles in the nucleus?

A) electrons
B) nucleons
C) positrons.
D) protons
E) neutrons

Question 6

Write the word or phrase that best completes each statement or answers the question.
Write the standard nuclear notation for the following nuclei: hydrogen-2, sulfur-33, and
lead-207.

Question 7

Choose the one alternative that best completes the statement or answers the question.
To a reasonable approximation, the density of a nucleus

A) is independent of the mass number.
B) varies unpredictably for different values of $Z$ .
C) is smaller for large-Z nuclei.
D) is qreater for large- $Z$ nuclei.

Question 8

Choose the one alternative that best completes the statement or answers the question.
The primary reason that very large nuclei are unstable is due to

A) the cumulative attractive force between the protons and the orbiting electrons.
B) the repulsive force between the neutrons and the protons.
C) the extreme weakness of the gravitational attraction of the protons.
D) the cumulative repulsive force of the protons.

Question 9

Choose the one alternative that best completes the statement or answers the question.
The atomic number and mass number for calcium-39 are 20 and 39, respectively. How many neutrons are in one atom?

A) 39
B) 19
C) 59
D) 20
E) 1

Question 10

Choose the one alternative that best completes the statement or answers the question.
A stable nucleus contains many protons very close to each other, all positively charged. Why do the protons not fly apart due to mutual Coulomb repulsion?

A) An attractive nuclear force in the nucleus counteracts the effect of the Coulomb forces.
B) The neutrons in the nucleus shield the protons from each other.
C) The Coulomb force does not operate within nuclei.
D) The gravity of the protons and neutrons overcomes their repulsion at such close distances.
E) There are an equal number of electrons in the nucleus which neutralize the protons.

Question 11

Choose the one alternative that best completes the statement or answers the question.
The symbol for a certain isotope of strontium is ${ } _ { 38 } ^ { 90 } \mathrm { Sr }$ . What is the mass number of this isotope?

A) 128
B) 90
C) 38
D) 88
E) 52

Question 12

Choose the one alternative that best completes the statement or answers the question.
In a ${ } _ { 41 } ^ { 93 } \mathrm { Nb }$ nucleus, how many protons, neutrons, and electrons are found there?

A) $52,41,41$ .
B) $41,52,93$ .
C) $93,41,93$ .
D) $41,52,41$ .
E) $41,52,0$ .

Question 13

Choose the one alternative that best completes the statement or answers the question.
If an atomic nucleus containing 64 nucleons has a radius $R$ , what will be the expected radius of a nucleus containing 512 nucleons?

A) $8 R$
B) $R$
C) $4 R$
D) $16 R$
E) $2 R$

Question 14

Choose the one alternative that best completes the statement or answers the question.
The atomic mass unit is defined as

A) one twelfth the mass of a carbon-12 atom.
B) the mass of an electron.
C) the mass of a carbon-12 nucleus.
D) the mass of a hydrogen-1 atom.
E) the mass of a proton.

Question 15

Write the word or phrase that best completes each statement or answers the question.
Name the first three isotopes of hydrogen, write their symbols in standard notation, and
indicate which one is the most common and which one is the most unstable.

Question 16

Choose the one alternative that best completes the statement or answers the question.
If an atomic nucleus containing 64 nucleons has a mass density $\rho$ , what will be the expected mass density of a nucleus containing 512 nucleons?

A) $8 \rho$
B) $16 \rho$
C) $\rho$
D) $4 \rho$
E) $2 \rho$

Question 17

Choose the one alternative that best completes the statement or answers the question.
The symbol for a certain isotope of polonium is ${ } _ { 84 } ^ { 214 }$ Po. How many neutrons are there in the nucleus of this isotope?

A) 314
B) 214
C) 84
D) 298
E) 130

Question 18

Choose the one alternative that best completes the statement or answers the question.
The mass number of an atom is equal to the number of what particles in the nucleus?

A) positrons.
B) electrons
C) nucleons
D) protons
E) neutrons

Question 19

Choose the one alternative that best completes the statement or answers the question.
All nuclei of a given element have the same number of

A) protons.
B) nucleons.
C) neutrons.
D) protons + neutrons.

Question 20

Choose the one alternative that best completes the statement or answers the question.
Which of the following statements is not true of the strong nuclear force?

A) For two protons that are very close together, the nuclear force and the electric force have about the same magnitudes.
B) A nucleon in a large nucleus interacts via the nuclear force only with nearby nucleons, not with ones far away in the nucleus.
C) The nuclear force affects both neutrons and protons.
D) The nuclear force has a short range, of the order of nuclear dimensions.
E) The nuclear force does not depend on charge.

Question 21

Choose the one alternative that best completes the statement or answers the question.
An $\alpha$ particle is also known as

A) a high-energy photon.
B) a positron.
C) a helium nucleus.
D) an electron.

Question 22

Choose the one alternative that best completes the statement or answers the question.
In $\beta ^ { - }$ decay, the number of neutrons in the nucleus is

A) increased by 2 .
B) decreased by $1 .$
C) decreased by $2 .$
D) increased by 1 .
E) remains unchanged.

Question 23

Write the word or phrase that best completes each statement or answers the question.
What are the mass number A and the charge (in units of e) for each of the following
particles or rays?
(a) beta-plus
(b) beta-minus
(c) gamma ray

Question 24

Choose the one alternative that best completes the statement or answers the question.
A gamma ray is also known as

A) a high-energy photon.
B) an electron.
C) a positron.
D) a helium nucleus.

Question 25

Choose the one alternative that best completes the statement or answers the question.
A fusion reaction releases energy because the binding energy of the resulting nucleus

A) is greater than the binding energy of the original nuclei.
B) is less than the binding energy of the original nuclei.
C) is equal to the binding energy of the original nuclei.
D) is released in the process.
E) is absorbed in the process.

Question 26

Choose the one alternative that best completes the statement or answers the question.
A $\beta ^ { + }$ particle is also known as

A) an electron.
B) a high-energy photon.
C) a positron.
D) a helium nucleus.

Question 27

Choose the one alternative that best completes the statement or answers the question.
During $\beta$ - decay

A) a proton is ejected from the nucleus.
B) the number of nucleons increases.
C) a neutron is transformed to a proton.
D) a proton is transformed to a neutron.
E) a neutron is ejected from the nucleus.

Question 28

Choose the one alternative that best completes the statement or answers the question.
In massive stars, three helium nuclei fuse together, forming a carbon nucleus, and this reaction heats the core of the star. The net mass of the three helium nuclei must therefore be

A) the same as that of the carbon nucleus because energy is always conserved.
B) less than that of the carbon nucleus.
C) the same as that of the carbon nucleus because mass is always conserved.
D) higher than that of the carbon nucleus.

Question 29

Choose the one alternative that best completes the statement or answers the question.
The nuclei of ${ } _ { 2 } ^ { 4 } \mathrm { He }$ are also known as

A) $\alpha$ particles.
B) positrons.
C) $\beta$ particles.
D) x-rays.
E) $\gamma$ rays.

Question 30

Choose the one alternative that best completes the statement or answers the question.
When a $\beta ^ { + }$ particle is emitted from an unstable nucleus, the atomic number of the nucleus

A) decreases by 1 .
B) decreases by $2 .$
C) increases by 1 .
D) increases by 2 .
E) does not change.

Question 31

Choose the one alternative that best completes the statement or answers the question.
When a $\beta$ - particle is emitted from an unstable nucleus, the atomic number of the nucleus

A) increases by 2 .
B) increases by 1 .
C) decreases by 1 .
D) decreases by 2 .
E) does not change.

Question 32

Choose the one alternative that best completes the statement or answers the question.
When a $\beta ^ { - }$ particle is emitted from an unstable nucleus, the atomic mass number of the nucleus

A) increases by 1 .
B) decreases by 2 .
C) decreases by 1 .
D) increases by 2 .
E) does not change.

Question 33

Choose the one alternative that best completes the statement or answers the question.
During $\beta ^ { + }$ decay

A) a proton is ejected from the nucleus.
B) a neutron is ejected from the nucleus.
C) the number of nucleons decreases.
D) a neutron is transformed to a proton.
E) a proton is transformed to a neutron.

Question 34

Choose the one alternative that best completes the statement or answers the question.
What is the mass number of alpha particles?

A) 1
B) 2
C) 3
D) 4
E) 6

Question 35

Write the word or phrase that best completes each statement or answers the question.
What are the mass number, the atomic number, and neutron number for each of the following particles?
(a) proton
(b) neutron
(c) alpha particle

Question 36

Choose the one alternative that best completes the statement or answers the question.
A $\beta$ - particle is also known as

A) a positron.
B) an electron.
C) a high-energy photon.
D) a helium nucleus.

Question 37

Choose the one alternative that best completes the statement or answers the question.
In beta-minus decay

A) an electron is emitted.
B) a proton is emitted.
C) a proton is transformed into a neutron.
D) a neutron is emitted.
E) an electron decays into another particle.

Question 38

Choose the one alternative that best completes the statement or answers the question.
The binding energy per nucleon of a nucleus

A) is approximately constant throughout the periodic table, except for very light nuclei.
B) decreases steadily as we go to heavier elements.
C) has a maximum near iron in the periodic table and decreases after that for heavier elements.
D) increases steadily as we go to heavier elements.
E) has a minimum near iron in the periodic table and increases after that for heavier elements.

Question 39

Choose the one alternative that best completes the statement or answers the question.
The two strongest forces that act between protons in a nucleus are

A) the weak nuclear and electromagnetic forces.
B) the electrostatic and the gravitational forces.
C) the weak nuclear and the gravitational forces.
D) the strong nuclear and the electrostatic forces.

Question 40

Choose the one alternative that best completes the statement or answers the question.
The main reason that there is a limit to the size of a stable nucleus is

A) the weakness of the electrostatic force.
B) the limited range of the gravitational force.
C) the short range nature of the strong nuclear force.
D) the weakness of the gravitational force.

Question 41

Choose the one alternative that best completes the statement or answers the question.
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?

A) The activities will be equal.
B) The activities cannot be compared without more information.
C) The activity of the strontium- 90 sample will be greater.
D) The activity of the cobalt-60 sample will be greater.

Question 42

Choose the one alternative that best completes the statement or answers the question.
In $\beta$ - decay, the number of protons in the nucleus is

A) decreased by 2 .
B) decreased by $1 .$
C) increased by $2 .$
D) increased by 1 .
E) remains unchanged.

Question 43

Choose the one alternative that best completes the statement or answers the question.
A $\beta ^ { - }$ decay occurs in an unstable nucleus when

A) a neutron is converted to an alpha particle by the weak force.
B) a proton is converted to a neutron by the strong force.
C) a proton is converted to an electron by the strong force.
D) a neutron is converted to a positron by the weak force.
E) a neutron is converted to a proton by the weak force.

Question 44

Choose the one alternative that best completes the statement or answers the question.
Modern in-air nuclear bomb tests have created an extra high level of ${ } ^ { 14 } \mathrm { C }$ 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?

A) Too young.
B) Correct, since ${ } ^ { 14 } \mathrm { C }$ from bomb tests is different from that produced naturally.
C) Correct, because modern biological materials do not gather ${ } ^ { 14 } \mathrm { C }$ from bomb tests.
D) Too old.

Question 45

Choose the one alternative that best completes the statement or answers the question.
Isotope A has a decay constant of $0.723 \mathrm {~s} ^ { - 1 }$ and isotope B has a decay constant of $0.514 \mathrm {~s} ^ { - 1 }$ . Which isotope has a longer half-life?

A) isotope $A$
B) isotope B

Question 46

Choose the one alternative that best completes the statement or answers the question.
What happens to the half-life of a radioactive substance as we increase its temperature?

A) It decreases at an exponential rate.
B) It decreases at a constant rate.
C) It increases.
D) It does not change.

Question 47

Choose the one alternative that best completes the statement or answers the question.
If the half-life of a material is 45 years, how much of it will be left after 100 years?

A) Iess than $1 / 2$ but more than $1 / 4$
B) more than $1 / 4$ but less than $1 / 2$
C) Iess than $1 / 4$ but more than $1 / 8$
D) Iess than $1 / 8$
E) more than $1 / 2$

Question 48

Choose the one alternative that best completes the statement or answers the question.
When an unstable nucleus decays by emitting an alpha particle, the atomic number $\mathrm { Z }$ of the nucleus

A) decreases by 4 .
B) decreases by 2 .
C) increases by $4 .$
D) increases by 2 .
E) remains unchanged.

Question 49

Choose the one alternative that best completes the statement or answers the question.
In positron decay, the number of protons in the nucleus is

A) decreased by $1 .$
B) increased by $2 .$
C) increased by $1 .$
D) decreased by 2 .
E) remains unchanged.

Question 50

Choose the one alternative that best completes the statement or answers the question.
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?

A) $2.5$ grams
B) more than $1.25$ grams but less than $2.5$ grams
C) $1.25$ grams
D) more than $2.5$ grams but less than 5 grams
E) Iess than $1.25$ grams

Question 51

Choose the one alternative that best completes the statement or answers the question.
Polonium-216 decays to lead-212 by emitting what kind of nuclear radiation?

A) alpha
B) beta-minus
C) $x$ -rays.
D) gamma
E) beta-plus

Question 52

Choose the one alternative that best completes the statement or answers the question.
What happens to the half-life of a radioactive substance as it decays?

A) It increases.
B) It decreases at a constant rate.
C) It remains constant.
D) It decreases at an exponential rate.

Question 53

Choose the one alternative that best completes the statement or answers the question.
The atom ${ } _ { 87 } ^ { 223 } \mathrm { Fr }$ decays to ${ } _ { 88 } ^ { 223 } \mathrm { Ra }$ by emitting what kind of nuclear radiation?

A) alpha
B) gamma
C) beta-plus
D) x-rays.
E) beta-minus

Question 54

Choose the one alternative that best completes the statement or answers the question.
A radioactive isotope of atomic number $Z$ emits a beta-minus particle, and then the daughter nucleus emits a gamma ray. What is the atomic number of the resulting nucleus after both processes?

A) $Z - 2$
B) $Z + 1$
C) $Z - 1$
D) $Z - 3$

Question 55

Choose the one alternative that best completes the statement or answers the question.
A radioactive isotope of atomic number $\mathrm { Z }$ emits an alpha particle, and the daughter nucleus then emits a beta-minus particle. What is the atomic number of the resulting nucleus?

A) $Z - 2$
B) $Z - 3$
C) $Z + 1$
D) $Z - 1$

Question 56

Write the word or phrase that best completes each statement or answers the question.
$$\text { How many protons, neutrons, and nucleons are there in a carbon-14 nucleus? }$$

Question 57

Choose the one alternative that best completes the statement or answers the question.
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?

A) There are more strontium-90 than cobalt-60 nuclei.
B) There are more cobalt-60 than strontium-90 nuclei.
C) There are equal numbers of cobalt-60 and strontium-90 nuclei.
D) It is not possible to compare numbers of nuclei without knowing the masses of the samples.

Question 58

Choose the one alternative that best completes the statement or answers the question.
Isotope A has a decay constant of $0.861 \mathrm {~s} ^ { - 1 }$ and isotope B has a decay constant of $0.627 \mathrm {~s} ^ { - 1 }$ . Which isotope has a longer mean life (time constant)?

A) isotope $A$
B) isotope B

Question 59

Choose the one alternative that best completes the statement or answers the question.
When an unstable nucleus decays by emitting an alpha particle, the atomic mass number $A$ of the nucleus

A) increases by 2 .
B) decreases by $2 .$
C) increases by $4 .$
D) decreases by 4 .
E) remains unchanged.

Question 60

Choose the one alternative that best completes the statement or answers the question.
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

A) predominantly to Y.
B) predominantly to X.
C) to X and Y equally.
D) entirely to Y.

Question 61

Choose the one alternative that best completes the statement or answers the question.
One of the fusion reactions that occurs in the sun is:
$${ } _ { 2 } ^ { 3 } \mathrm { He } + { } _ { 2 } ^ { 3 } \mathrm { He } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 1 } ^ { 1 } \mathrm { H } + { } _ { 1 } ^ { 1 } \mathrm { H }$$
The following atomic masses are known:
${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.007825 \mathrm { u }$
${ } _ { 2 } ^ { 3 } \mathrm { He } : \quad 3.016029 \mathrm { u }$
${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$
What is the reaction energy released in this fusion reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

A) $19 \mathrm { MeV }$
B) $13 \mathrm { MeV }$
C) $15 \mathrm { MeV }$
D) $11 \mathrm { MeV }$
E) $17 \mathrm { MeV }$

Question 62

Choose the one alternative that best completes the statement or answers the question.
The following masses are known:
$$\begin{array} { l l } { } _ { 0 } ^ { 1 } \mathrm { n } & 1.008665 \mathrm { u } \\{ } _ { 1 } ^ { 1 } \mathrm { H } & 1.007825 \mathrm { u } \\{ } _ { 88 } ^ { 226 } \mathrm { Ra } & 226.025403 \mathrm { u }\end{array}$$
What is the binding energy of ${ } _ { 88 } ^ { 226 } \mathrm { Ra }$ ? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

A) $2500 \mathrm { MeV }$
B) $2300 \mathrm { MeV }$
C) $1900 \mathrm { MeV }$
D) $1700 \mathrm { MeV }$
E) $2100 \mathrm { MeV }$

Question 63

Choose the one alternative that best completes the statement or answers the question.
Calculate the estimated nuclear radius of ${ } _ { 38 } ^ { 90 } \mathrm { Sr } ?$

A) $5.4 \times 10 ^ { - 15 } \mathrm {~m}$
B) $4.0 \times 10 ^ { - 15 } \mathrm {~m}$
C) $1.1 \times 10 ^ { - 13 } \mathrm {~m}$
D) $1.2 \times 10 ^ { - 15 } \mathrm {~m}$
E) $3.3 \times 10 ^ { - 13 } \mathrm {~m}$

Question 64

Choose the one alternative that best completes the statement or answers the question.
Estimate the radius of a nucleus with mass $50 \mathrm { u }$ . ( $m _ { \text {neutron } } \approx m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ )

A) about $4.4 \mathrm { fm }$
B) about $3.7 \mathrm { fm }$
C) about $6.2 \mathrm { fm }$
D) about $8.5 \mathrm { fm }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
The diameter of an atom is $1.4 \times 10 ^ { - 10 } \mathrm {~m}$ and the diameter of its nucleus is $1.0 \times 10 ^ { - 14 } \mathrm {~m}$ . What fraction of the atom's volume is occupied by its nucleus?

A) $7.1 \times 10 ^ { - 5 }$
B) $5.1 \times 10 ^ { - 9 }$
C) $3.6 \times 10 ^ { - 13 }$
D) $2.6 \times 10 ^ { - 17 }$

Question 66

Choose the one alternative that best completes the statement or answers the question.
An excited ${ } _ { 92 } ^ { 236 } \mathrm { U } ^ { * }$ nucleus undergoes fission into two fragments as follows:
$${ } _ { 92 } ^ { 236 } \mathrm { U } ^ { * } \rightarrow { } _ { 56 } ^ { 144 } \mathrm { Ba } + { } _ { 36 } ^ { 92 } \mathrm { Kr }$$
If, at the instant of fission, the $\mathrm { Ba }$ and $\mathrm { Kr }$ fragments are spherical and just barely in contact, what is the electrostatic potential energy of these two fragments? ( $1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C }$ , $1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $270 \mathrm { MeV }$
B) $240 \mathrm { MeV }$
C) $260 \mathrm { MeV }$
D) $230 \mathrm { MeV }$
E) $250 \mathrm { MeV }$

Question 67

Write the word or phrase that best completes each statement or answers the question.
How much energy is released when $0.60 \mu \mathrm { g }$ of $3 \mathrm { H }$ have decayed to $3 \mathrm { He }$ ? The mass of $3 \mathrm { He }$ is $3.0160293 \mathrm { u }$ , the mass of $3 \mathrm { H }$ is $3.0160492 \mathrm { u } , 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ , and $\mathrm { N } _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol }$ .

Question 68

Choose the one alternative that best completes the statement or answers the question.
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? $( 1 \mathrm { eV } = 1.60$ $\times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $3.39 \times 10 ^ { - 12 } \mathrm {~m}$
B) $6.56 \times 10 ^ { - 15 } \mathrm {~m}$
C) $2.81 \times 10 ^ { - 14 } \mathrm {~m}$
D) $2.17 \times 10 ^ { - 14 } \mathrm {~m}$

Question 69

Choose the one alternative that best completes the statement or answers the question.
Carbon-14 decays by $\beta ^ { - }$ emission. What nucleus is left after this decay?

A) nitrogen-14
B) nitrogen-15
C) carbon-14
D) carbon-15
E) carbon-13

Question 70

Choose the one alternative that best completes the statement or answers the question.
Estimate the mass of a nucleus with radius $2.8 \times 10 ^ { - 15 } \mathrm {~m} . \left( 1 \mathrm { u } = 1.6605 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A) about $2.1 \times 10 ^ { - 26 } \mathrm {~kg}$
B) about $4.7 \times 10 ^ { - 26 } \mathrm {~kg}$
C) about $2.3 \times 10 ^ { - 26 } \mathrm {~kg}$
D) about $7.5 \times 10 ^ { - 27 } \mathrm {~kg}$

Question 71

Write the word or phrase that best completes each statement or answers the question.
Estimate the radius (in fm) of a radon nucleus that contains 86 protons and 136 neutrons.

Question 72

Choose the one alternative that best completes the statement or answers the question.
A beryllium-8 nucleus at rest undergoes double alpha decay as follows:
$${ } _ { 4 } ^ { 8 } \mathrm { Be } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 2 } ^ { 4 } \mathrm { He }$$
The known atomic masses are:
${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$
${ } _ { 4 } ^ { 8 } \mathrm { Be } : \quad 8.005305 \mathrm { u }$
What is the kinetic energy of each departing alpha particle? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$

A) $130 \mathrm { keV }$
B) $92 \mathrm { keV }$
C) $180 \mathrm { keV }$
D) $46 \mathrm { keV }$
E) $65 \mathrm { keV }$

Question 73

Choose the one alternative that best completes the statement or answers the question.
Calculate the estimated density of the nucleus of ${ } _ { 38 } ^ { 90 } \mathrm { Sr } ? \left( m _ { \text {neutron } } \approx m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right.$ )

A) greater than $3.0 \times 10 ^ { 20 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $2.3 \times 10 ^ { 17 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $2.0 \times 10 ^ { 15 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $2.1 \times 10 ^ { 19 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $90 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 74

Write the word or phrase that best completes each statement or answers the question.
What is the approximate nuclear radius of an isotope of sodium with 11 protons and 12
neutrons?

Question 75

Write the word or phrase that best completes each statement or answers the question.
How many nucleons would you expect a nucleus to contain if its diameter is 13.4 fm?

Question 76

Write the word or phrase that best completes each statement or answers the question.
The radius $R$ of a nucleus of mass number $A$ is given by $R = R _ { 0 } A ^ { 1 / 3 }$ , where $R _ { 0 } = 1.2 \times$ $10 ^ { - 15 } \mathrm {~m}$ , calculate the density of a nucleus that has contains 57 protons and 82 neutrons. The mass of a nucleon (proton or neutron) is $1.67 \times 10 ^ { - 27 } \mathrm {~kg}$ .

Question 77

Choose the one alternative that best completes the statement or answers the question.
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 $55 \mathrm { MeV }$ , 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. $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \right.$ $\cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A) $0 \mathrm { fm }$
B) $0 \mathrm { fm }$
C) $0 \mathrm { fm }$
D) $0 \mathrm { fm }$

Question 78

Write the word or phrase that best completes each statement or answers the question.
What should be the approximate diameter (in fm) of a nucleus containing 92 protons and
143 neutrons?

Question 79

Choose the one alternative that best completes the statement or answers the question.
A summary of the nuclear reactions that power our sun is $4 \mathrm { p } \rightarrow 4 \mathrm { He } + 2 \mathrm { e } ^ { - }$ , with masses of $938.272$ $\mathrm { MeV } / \mathrm { c } ^ { 2 }$ for a proton, $3727.38 \mathrm { MeV } / \mathrm { c } ^ { 2 }$ for the helium nucleus, and $0.511 \mathrm { MeV } / \mathrm { c } ^ { 2 }$ for each electron. How much energy is released by each of these reactions?

A) $28.3 \mathrm { MeV }$
B) $2790.13 \mathrm { MeV }$
C) $279.01 \mathrm { MeV }$
D) $24.69 \mathrm { MeV }$

Question 80

Choose the one alternative that best completes the statement or answers the question.
A proton is projected at a stationary ${ } _ { 88 } ^ { 226 }$ Ra aluminum target. The proton momentarily comes to a halt at a distance from the center of an aluminum nucleus, equal to twice the nuclear radius. Assume that the nucleus retains its spherical shape and that the nuclear force on the proton is negligible. The initial kinetic energy of the proton, in $\mathrm { MeV }$ , is closest to:

A) $5.8 \mathrm { MeV }$
B) $2.9 \mathrm { MeV }$
C) $8.7 \mathrm { MeV }$
D) $13 \mathrm { MeV }$
E) $17 \mathrm { MeV }$