Deck 42: Nuclear Physics

Question 1

Let Z denote the atomic number and A denote the mass number of a nucleus. The number of neutrons in this nucleus is:

A) Z
B) A - Z
C) A - 2Z
D) A
E) 2A - Z

Answer 1

A - Z

Question 2

The isotopes of an element:

A) cannot be separated at all
B) occur well separated in nature
C) have similar chemical behavior
D) cannot be separated by physical methods
E) have equal masses

Answer 2

have similar chemical behavior

Question 3

Stable nuclei generally:

A) have a greater number of protons than neutrons
B) have low mass numbers
C) have high mass numbers
D) are beta emitters
E) none of the above

Answer 3

none of the above

Question 4

A nucleus with a mass number of 64 has a mean radius of about:

A) 4.8 fm
B) 9.6 fm
C) 77 fm
D) 260 fm
E) 2.6 * 10⁵ fm

Question 5

Iron has atomic number 26. Naturally mined iron contains isotopes of mass numbers 54, 56, 57, and 58. Which of the following statements is FALSE?

A) every atom of iron has 26 protons
B) some iron atoms have 30 neutrons
C) some iron atoms have 54 neutrons
D) the isotopes may be separated in a mass spectrometer
E) there are four kinds of naturally occurring iron atoms with the same chemical properties

Question 6

The greatest binding energy per nucleon occurs for nuclides with masses near that of:

A) helium
B) sodium
C) iron
D) mercury
E) uranium

Question 7

In the Rutherford scattering experiment, an alpha particle is aimed directly at a gold nucleus. The distance of closest approach of the alpha particle to the nucleus occurs when:

A) the alpha particle hits the nucleus
B) the alpha particle hits the electron cloud
C) the kinetic energy of the alpha particle is completely transformed to potential energy due to the nuclear force
D) the kinetic energy of the alpha particle is completely transformed to potential energy due to the electric field of the nucleus
E) the kinetic energy of the alpha particle is completely transformed to potential energy due to the electric field of the electrons

Question 8

1 atomic mass unit is about:

A) 1.66 *10^-31 kg
B) 9.11 * 10^-31 kg
C) 1.66 *10^-27 kg
D) 9.11 *10^-27 kg
E) 1.66 * 10^-25 kg

Question 9

A proton in a large nucleus:

A) has a net attractive force on all other protons in the nucleus
B) has a net repulsive force on all other protons in the nucleus
C) has a net repulsive force on all other neutrons in the nucleus
D) has a net attractive force on some protons in the nucleus and a net repulsive force on others
E) has a net attractive force on some neutrons in the nucleus and a net repulsive force on others

Question 10

Volumes of atomic nuclei are proportional to:

A) the mass number
B) the atomic number
C) the total nuclear spin
D) the number of neutrons
E) none of these

Question 11

If a nucleus has mass M, Z protons (mass m_p) and N neutrons (mass m_n) its binding energy is equal to:

A) Mc²
B) (M - Zm_p - Nm_n)c²
C) (Zm_p + Nm_n - M)c²
D) (Zm_p + Nm_n)c²
E) (Zm_p - M)c²

Question 12

The binding energy of a nucleus is the energy that must be supplied to:

A) remove a nucleon
B) remove an alpha particle
C) remove a beta particle
D) separate the nucleus into its constituent nucleons
E) separate the nucleus into a collection of alpha particles

Question 13

The smallest particle of any chemical element that can exist by itself and yet retain the qualities that distinguish it as that element is:

A) an electron
B) a proton
C) a neutron
D) an atom
E) a molecule

Question 14

Which of the following nuclides is least stable?

A) ⁵²Fe (Z = 26)
B) ¹¹⁵Nd (Z = 60)
C) ¹⁷⁵Lu (Z = 71)
D) ²⁰⁸Pb (Z = 82)
E) ²³⁸U (Z = 92)

Question 15

Let A be the mass number and Z be the atomic number of a nucleus. Which of the following is approximately correct for light nuclei?

A) Z = 2A
B) Z = A
C) Z = A/2
D) Z =
E) Z = A²

Question 16

The mass density of an atomic nucleus:

A) is about 10¹⁵ kg/m³
B) is about 10¹² kg/m³
C) increases with increasing nuclear mass
D) increases with decreasing nuclear radius
E) is roughly constant independent of atomic number

Question 17

The atomic number of an element is:

A) the whole number nearest to its mass
B) the number of protons in its nucleus
C) the nearest whole number of hydrogen atoms having the same mass as a single atom of the given element
D) the number of neutrons in its nucleus
E) its order of discovery

Question 18

A femtometer is:

A) larger than 10^-9 m
B) 10^-9 m
C) 10^-12 m
D) 10^-15 m
E) 10^-18 m

Question 19

Bromine, with atomic mass 79.942 u, is composed of nearly equal amounts of two isotopes, one of which contains 79 nucleons per atom. The mass number of the other isotope is:

A) 78
B) 79
C) 80
D) 81
E) 82

Question 20

The Rutherford scattering experiment showed that:

A) light has both particle-like and wavelike properties
B) atoms are electrically neutral
C) the positive and negative charges in the atom are uniformly distributed throughout its volume
D) the wavelength of scattered light depends on the scattering angle
E) the atom consists of a very tiny, massive, positively charged nucleus surrounded by almost empty space

Question 21

Starting with a sample of pure ⁶⁶Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding half-life is:

A) 3.75 minutes
B) 5 minutes
C) 7 minutes
D) 10 minutes
E) 15 minutes

Question 22

Two protons are about 10^-10 m apart. Their relative motion is chiefly determined by:

A) gravitational forces
B) electrical forces
C) nuclear forces
D) magnetic forces
E) torque due to electric dipole moments

Question 23

At the end of 14 min, 1/16 of a sample of radioactive polonium remains. The corresponding half-life is:

A) (7/8) min
B) (8/7) min
C) (7/4) min
D) (7/2) min
E) (14/3) min

Question 24

The half-life of a radioactive isotope is 6.5 h. If there are initially 48 * 10³² atoms of this isotope, the number of atoms of this isotope remaining after 26 h is:

A) 12 * 10³²
B) 6 * 10³²
C) 3 * 10³²
D) 6 *10⁴
E) 3 * 10²

Question 25

A large collection of nuclei are undergoing alpha decay. The rate of decay at any instant is proportional to:

A) the number of undecayed nuclei present at that instant
B) the time since the decays started
C) the time remaining before all have decayed
D) the half-life of the decay
E) the average time between decays

Question 26

The relationship between the activity R, the disintegration constant λ, and the remaining number N of radioactive nuclei is:

A) N = λR
B) R = λN
C) R = λ/N
D) R = N/ λ
E) R = λ ln N

Question 27

²¹⁰Bi (an isotope of bismuth) has a half-life of 5.0 days. The time for three-quarters of a sample of ²¹⁰Bi to decay is:

A) 2.5 days
B) 3.75 days
C) 10 days
D) 15 days
E) 20 days

Question 28

The half-life of a radioactive substance is:

A) half the time it takes for the entire substance to decay
B) usually about 50 years
C) the time for radium to change into lead
D) calculated from E = mc²
E) the time for half the substance to decay

Question 29

Possible units for the disintegration constant $\lambda$ are:

A) kg/s
B) s/kg
C) hour
D) day^-1
E) cm^-1

Question 30

One curie is equivalent to:

A) one Becquerel
B) one decay per second
C) 3.0 x 10⁸ decays per second
D) 3.7 x 10¹⁰ decays per second
E) 10⁶ Becquerel

Question 31

Which expression correctly describes the radioactive decay of a substance whose half-life is T?

A) N(t) = N₀e^{-(t ln2)/T}
B) N(t) = N₀e^-t/T
C) N(t) = N₀e^-tT
D) N(t) = N₀e^{-tT ln2}
E) N(t) = N₀e^{-t/T ln2}

Question 32

The half-life of a radioactive isotope is 140 days. In how many days does the decay rate of a sample of this isotope decrease to one fourth its initial decay rate?

A) 35 days
B) 70 days
C) 105 days
D) 210 days
E) 280 days

Question 33

The half-life of radium is about 1600 years. If a rock initially contains 1 g of radium, the amount left after 8000 years will be about:

A) 200 mg
B) 63 mg
C) 31 mg
D) 16 mg
E) less than 1 mg

Question 34

The half-life of a given nuclear disintegration A $\rightarrow$ B:

A) depends on the initial number of A atoms
B) depends on the initial number of B atoms
C) is an exponentially increasing function of time
D) is an exponentially decreasing function of time
E) none of the above

Question 35

The graph shows the decay rate R as a function of the time t for three radioactive samples. Rank the samples according to their half-lives, shortest to longest.

A) 1, 2 ,3
B) 1, 3, 2
C) 2, 1, 3
D) 2, 3, 1
E) 3, 1, 2

Question 36

In an alpha decay the disintegration energy appears as:

A) photon energies
B) the kinetic energies of the alpha and the daughter nucleus
C) the excitation energy of the daughter nucleus
D) the excitation energy of the alpha particle
E) heat

Question 37

Radioactive ⁹⁰Sr has a half-life of 30 years. What percent of a sample of ⁹⁰Sr will remain after 60 years?

A) 0%
B) 14%
C) 25%
D) 50%
E) 75%

Question 38

Radioactive element A decays to the stable element B with a half-life T. Starting with a sample of pure A and no B, which graph below most correctly shows the number of A atoms, N_A, as a function of time t?

A) I
B) II
C) III
D) IV
E) V

Question 39

Two protons are separated by 10^-16 m. The nuclear (N), electrostatic (E), and gravitational (G) forces between these protons when written in order of increasing strength are:

A) N, E, G
B) N, G, E
C) G, E, N
D) G, N, E
E) E, G, N

Question 40

The relation between the disintegration constant $\lambda$ and the half-life T of a radioactive substance is:

A) $\lambda$ = 2T
B) $\lambda$ = 1/T
C) $\lambda$ = 2/T
D) $\lambda$ T = ln 2
E) $\lambda$ T = ln(1/2)

Question 41

An alpha particle is:

A) a helium atom with two electrons removed
B) an aggregate of two or more electrons
C) a hydrogen atom
D) the ultimate unit of positive charge
E) sometimes negatively charged

Question 42

Aluminum has atomic number 13, helium has atomic number 2, and silicon has atomic number 14. In the nuclear reaction ²⁷Al + ⁴He $\rightarrow$ ³⁰Si + ( ) the missing particle is:

A) an $\alpha$ particle
B) a positron
C) an electron
D) a proton
E) a neutron

Question 43

A radium atom, ²²⁶Ra (Z = 86), emits an alpha particle. The number of protons in the resulting atom is:

A) 84
B) 85
C) 86
D) 88
E) some other number

Question 44

Radioactive polonium, ²¹⁴Po (Z = 84), decays by alpha emission to:

A) ²¹⁴Po (Z = 84)
B) ²¹⁰Pb (Z = 82)
C) ²¹⁴At (Z = 85)
D) ²¹⁸Po (Z = 84)
E) ²¹⁰Bi (Z = 83)

Question 45

The energies of electrons emitted in $\beta$ ^- decays have a continuous spectrum because:

A) the original neutron has a continuous spectrum
B) the neutrino can carry off energy
C) the emitted electron is free
D) energy is not conserved
E) the daughter nucleus may have any energy

Question 46

A certain nucleus, after absorbing a neutron, emits a $\beta$ ^- and then splits into two alpha particles. The (A, Z) of the original nucleus must have been:

A) 6, 2
B) 6, 3
C) 7, 2
D) 7, 3
E) 8, 4

Question 47

A beta particle is:

A) a helium nucleus
B) an electron or a positron
C) a radioactive element
D) any negative particle
E) a hydrogen atom

Question 48

A nucleus with mass number A and atomic number Z undergoes $\beta$ ^- decay. The mass number and atomic number, respectively, of the daughter nucleus are:

A) A, Z - 1
B) A - 1, Z
C) A + 1, Z - 1
D) A, Z + 1
E) A, Z

Question 49

Some alpha emitters have longer half-lives than others because:

A) their alpha particles have greater mass
B) their alpha particles have less mass
C) their barriers to decay are higher and wider
D) their barriers to decay are lower and narrower
E) their decays include the emission of a photon

Question 50

An atom of ²³⁵U (Z = 92) disintegrates to ²⁰⁷Pb (Z = 82) with a half-life of about a billion years by emitting seven alpha particles and ______ $\beta$ ^- particles:

A) 3
B) 4
C) 5
D) 6
E) 7

Question 51

In addition to the daughter nucleus and an electron or positron, the products of a beta decay include:

A) a neutron
B) a neutrino
C) a proton
D) an alpha particle
E) no other particle

Question 52

A nucleus with mass number A and atomic number Z emits an alpha particle. The mass number and atomic number, respectively, of the daughter nucleus are:

A) A, Z -2
B) A - 2, Z - 2
C) A - 2, Z
D) A - 4, Z
E) A - 4, Z - 2

Question 53

A nucleus with mass number A and atomic number Z undergoes $\beta$ ⁺ decay. The mass number and atomic number, respectively, of the daughter nucleus are:

A) A - 1, Z - 1
B) A - 1, Z + 1
C) A + 1, Z - 1
D) A, Z + 1
E) A, Z - 1

Question 54

Magnesium has atomic number 12, hydrogen has atomic number 1, and helium has atomic number 2. In the nuclear reaction ²⁴Mg + ²H $\rightarrow$ ( ) + ⁴He the missing quantity is:

A) ²³Na (Z = 11)
B) ²²Ne (Z = 10)
C) ²¹Na (Z = 11)
D) ²¹Ne (Z = 10)
E) ²²Na (Z = 11)

Question 55

Rank the following collections of particles according to the total binding energy of all the particles in each collection, least to greatest.

A) 1,2,3
B) 3,2,1
C) 2,1,3
D) 1,3,2
E) 2,3,1

Question 56

The ⁶⁶Cu (Z = 29) produced in a nuclear bombardment is unstable, changing to ⁶⁶Zn (Z = 30) by the emission of:

A) a proton
B) a gamma ray photon
C) a positron
D) an electron
E) an alpha particle

Question 57

Bombardment of ²⁸Si (Z = 14) with alpha particles may produce:

A) a proton and ³¹P (Z = 15)
B) hydrogen and ³²S (Z = 16)
C) a deuteron and ²⁷Al (Z = 13)
D) helium and ³¹P (Z = 15)
E) ³⁵Cl (Z = 17)

Question 58

A radioactive atom X emits a $\beta$ ^- particle. The resulting atom:

A) must be very reactive chemically
B) has an atomic number that is one more than that of X
C) has a mass number that is one less than that of X
D) has an atomic number that is one less than that of X
E) is the same chemical element as X

Question 59

Beta particles from various radioactive sources all have:

A) the same mass
B) the same speed
C) the same charge
D) the same deflection
E) the same energy in a magnetic field

Question 60

If ²⁰⁴Tl (Z = 81) emits a $\beta$ ^- particle from its nucleus:

A) stable Tl is formed
B) ²⁰²Hg (Z = 80) is formed
C) ²⁰⁴Pb (Z = 82) is formed
D) radioactive Tl is formed
E) ¹⁹⁷Au (Z = 79) is formed

Question 61

A typical mammogram X-ray results in a radiation dose equivalent of 70 mrem. What absorbed dose does this correspond to?

A) 70 mGy
B) 70 Sv
C) 7.0 Gy
D) 0.70 Sv
E) 0.70 Gy

Question 62

The gray is the correct unit to use in reporting the measurement of:

A) the rate of decay of a radioactive source
B) the ability of a beam of gamma ray photons to produce ions in a target
C) the energy delivered by radiation to a target
D) the biological effect of radiation
E) none of the above

Question 63

The sievert is the correct unit to use in reporting the measurement of:

A) the rate of decay of a radioactive source
B) the ability of a beam of gamma ray photons to produce ions in a target
C) the energy delivered by radiation to a target
D) the biological effect of radiation
E) none of the above

Question 64

The becquerel is the correct unit to use in reporting the measurement of:

A) the rate of decay of a radioactive source
B) the ability of a beam of gamma ray photons to produce ions in a target
C) the energy delivered by radiation to a target
D) the biological effect of radiation
E) none of the above

Question 65

The model of the nucleus in which each nucleon has its own well-defined quantum numbers is called the:

A) collective model
B) quantum model
C) liquid drop model
D) independent model
E) atomic model

Question 66

Magic nucleon numbers are associated with:

A) nuclei that decay via alpha decay
B) nuclei that decay via beta decay
C) nuclei that have equal numbers of protons and neutrons
D) nuclei that are relatively stable
E) nuclei that fission readily

Question 67

A fly caught in amber is thought to be 3 million years old. Why would it not be useful to confirm its age using radiocarbon dating?

A) The fly contains no carbon.
B) The fly is too small to contain a measurable amount of carbon.
C) The fly is too old to contain a measureable amount of carbon-14.
D) The carbon-14 doesn't begin to decay until the fly is removed from the amber.
E) Radiocarbon dating is too inaccurate to be useful.

Question 68

⁴⁰K decays to ⁴⁰Ar with a half-life of 1.25 x 10⁹ yr. Assume that rocks contain no ⁴⁰Ar when they form, and that the only way ⁴⁰Ar can be present is through the decay of ⁴⁰K. If the ratio of ⁴⁰K to ⁴⁰Ar in a particular rock is found to be 1:3, what is the age of the rock?

A) 1.25 x 10⁹ yr
B) 2.50 x 10⁹ yr
C) 3.75 x 10⁹ yr
D) 5.00 x 10⁹ yr
E) cannot be determined without knowing how much ⁴⁰K was in the rock to begin with