Nuclear physics is part of physics that tells about the interactions in the atomic nuclei. There are lots of concepts since its a vast subject like radioactivity, decay rate, half life period, nuclear reactions like fusion and fission. So only important formulas are discussed here.

If initially No number of atoms are present then,
Number of atoms = No = N + ND.
Where,
N = No of Atoms that remains after time t,
ND = No of atoms that gets decayed at time t.

Decay rate depends on rate of change in number of atoms to the time t.
It is given by,
Activity A = $\frac{dN}{dt}$.
or 
Activity A =  $\lambda$ N.
Where,
N = No of Atoms that remains after time t,
$\lambda$ is decay constant. 

Decay constant formula is,
Decay constant $\lambda$ = $\frac{A}{N}$.
Where,
A is activity and N is the no of atoms remaining.

Half-life period t1/2 of the radio isotope is given by,
t1/2 = $\frac{0.693}{\lambda}$.
Where, $\lambda$ is decay constant.

Mean life time of an atom before decay is given by,
$\tau$ = $\frac{1}{\lambda}$.
Where, $\lambda$ is decay constant.

Mass number A formula is given by,
A = Z + N.
Where, Z is number of protons,
N is neutrons.

Nuclear radius R formula is given by,
R = Ro A1/3.
Where, Ro is radius of nucleon (1.3 fm),
A is nucleon number.

Below are given some sample problems on nuclear physics you can go through:

Question 1: The Half life period of yttrium is 19 min 30 sec. If 780 gms of yttrium are present, what will be left after 25 min?
Solution:
Given:
Initial amt of radioactive elements, No = 780 gms,
Half life period, t1/2 = 19 min 30 sec,
time taken, t = 25 min

To find decay constant $\lambda$,
$\lambda$ = $\frac{0.693}{t_{1/2}}$
    
$\lambda$ = $\frac{0.693}{19.5}$
                  
$\lambda$ = 0.035

Finally to find the decay rate,
N$_{t}$ = No e$^{-\lambda \ t}$
N$_{t}$ = 780 $\times$ e$^{-0.035 \times 25 \ min}$
N$_{t}$ = 1871.12 gms

$\therefore$ 1871.12 gms of Yttrium left after 25 min.

Question 2: If the atomic number of the element is 7 and neutron number is 8. Calculate its mass number.
Solution:
Given:
Atomic number z = 7, neutron number N = 8

Mass number A is given by,
A = Z + N
A = 7 + 8
A = 15.

Therefore, 15 is the mass number of the given element.