Radioactivity

Question 1

What is the typical size of a nucleus?

Answer 1

About 10^-15 m (1 femtometre).

Question 2

What range can nuclear half-lives span?

Answer 2

From 10^-20 seconds to longer than the age of the Universe.

Question 3

What are the typical nuclear energy units?

Answer 3

MeV (mega-electronvolts).

Question 4

Define radioactive decay.

Answer 4

The spontaneous emission of radiation(s) that changes the state of the nucleus to more stable.

Question 5

What is the nuclear notation A_Z X?

Answer 5

A nucleus with atomic number Z (protons), mass number A (protons + neutrons), and symbol X.

Question 6

What are isotopes?

Answer 6

Nuclei with the same number of protons (Z) but different numbers of neutrons (N).

Question 7

What are the main types of decay and their emissions?

Answer 7

α decay: Helium nucleus (4/2 He); β decay: electron or positron; γ decay: photon.

Question 8

Which nuclei tend to undergo α decay?

Answer 8

Heavier nuclei (large Z, number of protons).

Question 9

Which nuclei tend to undergo β decay?

Answer 9

Lighter nuclei with neutron or proton imbalance.

Question 10

Define activity.

Answer 10

Rate at which decay occurs. The number of radioactive decays per second.

Question 11

What are the SI of activity?

Answer 11

SI: Becquerel (1 Bq = 1 decay/s)

Question 12

Formula for activity?

Answer 12

A = λN

Question 13

Differential equation describing decay?

Answer 13

dN/dt = -λN

Question 14

Exponential decay law?

Answer 14

N = N0 e^(-λt)

Question 15

Half-life formula?

Answer 15

t1/2 = ln(2)/λ

Question 16

Mean lifetime formula?

Answer 16

τ = 1/λ

Question 17

What is a decay chain?

Answer 17

A series of decays where one unstable nucleus transforms into another until stability.

Question 18

Example of decay sequence differential equations?

Answer 18

dNA/dt = -λA NA,
dNB/dt = λA NA - λB NB

B is produced at the rate A decays

Question 19

General equation for α decay?

Answer 19

^A_Z X → ^{A−4}_{Z−2} Y + ^4_2 He

Question 20

Energy released (Q value) formula?

Answer 20

Q = [ΣMreactants − ΣMproducts] c²

Question 21

Condition for spontaneous decay?

Answer 21

Q > 0

Question 22

Why α particles released rather than nucleus with say 1 proton and 2 neutrons?

Answer 22

They are highly stable and energetically favorable for emission.

Question 23

What is the Geiger-Nuttall rule?

Answer 23

Higher α-particle energy → shorter half-life.

Question 24

What are the three types of β decay?

Answer 24

β−: n→p+e−+ν̄e; β+: p→n+e++νe; Electron capture: p+e−→n+νe.

Question 25

Why is the β spectrum continuous?

Answer 25

Because energy is shared between the electron/positron and neutrino. Emitted electrons/positrons have a range of energies

Question 26

What is γ decay?

Answer 26

De-excitation of a nucleus by emission of a photon without changing A or Z.

Question 27

what is e^2/(4,pi,epsilon0)

Answer 27

1.440MeV fm

Question 28

what is hbar c

Answer 28

197

Question 29

why does more neutrons mean more stable?

Answer 29

to overcome coulomb interaction. too many protons will repel, the strong nuclear force doesn't hold them as strongly as coulomb interaction repels them. larger nuclei need more neutrons as these have no repulsive forces

Question 30

conversion between nuclear and atomic masses

Answer 30

Mn = Ma - Zm_e

Question 31

what does the Geiger-Nuttall rule assume?

Answer 31

alpha particle preformed inside nucleus and moves in spherical potential well

Question 32

Alpha decay potential V(r)

Answer 32

V = (Z_1 Z_2 e^2)/(4 pi epsilon0 r)

Question 33

Define the potential well for alpha decay

Answer 33

classically confined to potential well (r < a) with depth -V_0 Region with a

Question 34

Alpha decay potential B?

Answer 34

B = barrier height B= (1/4 pi epsilon_0)(2(Z-2)e^2/a) comes from normal V using Z_1 and 2 and Z_2 as Z-2 and r as a

Question 35

Alpha decay potential b

Answer 35

b = (1/4 pi epsilon_0)(2(Z-2)e^2/Q)

Question 36

How do we approximate the alpha decay potential

Answer 36

step potential (B-Q)/2 and (b-a)/2

Question 37

what is orbital electron capture

Answer 37

inner shell electron is captured by a proton, turns into a neutron, releases neutrino occurs in proton rich nuclei