Formula Sheet

## Nuclei

- All the formula of the chapter in one go
1
Nuclear Composition and Atomic Mass
Z - atomic number = number of protons
N - neutron number = number of neutrons
A - mass number = Z + N = total number of protons and neutrons

Nuclear Notation:
where X is the chemical Symbol of the element

1 Atomic mass unit (1u)=
Mass of proton,
Mass of neutron,
2
Size of Nucleus

Volume of a nucleus:

Density of Nucleus(ignoring mass difference between proton and neutron:

3
Mass Defect and Binding Energy
Mass defect:
M=Mass of Nucleus
=Mass of proton
=Mass of neutron
Binding energy:
Binding energy per nucleon:
A<30: small; unstable
30
A>170: small; unstable
4
N(t): Number of active nuclei at time t
: Number of active nuclei at t=0
: decay constant
The decay rate R of a radioactive substance is
SI unit: becquerel (bq) ; Other units: curie(ci), rutherford(rd)
Half life:
After n half lives:
a. number of nuclei left=
b. fraction of nuclei left=
c. percentage of nuclei left=
Number of nuclei decayed after time t:
Probability of nucleus for survival at time t:
Probability of Nucleus for disintegration at time t:
5
Decay Schemes
Alpha decay
Q value of alpha decay
mass defect=
Beta Decay:
Example:
Example: