Q: State the radioactive decay law. Derive mathematically the exponential decay law expression $N(t) = N0 e^{-\lambda t}$ for a radioactive substance.

Statement of Radioactive Decay Law:\nAt any instant, the rate of decay of radioactive nuclei (i.e., the number of nuclei decaying per unit time) is directly proportional to the number of undecayed radioactive nuclei present at that instant. Derivation:\nLet $N$ be the number of undecayed radioactive

Question 1

Define atomic mass unit (amu) and calculate the energy equivalent of 1 amu in mega-electron volts (MeV).

Accepted Answer

Atomic mass unit (amu), or unified atomic mass unit (u), is defined as one-twelfth ($1/12^{	ext{th}}$) of the mass of an unbound neutral carbon-12 atom in its nuclear and electronic ground state. Its standard value is approximately $1.660539 	imes 10^{-27}$ kg. 
To find the energy equivalent of 1

Question 2

Explain the phenomenon of nuclear fission with a suitable example and state how energy is released in the process.

Accepted Answer

Nuclear fission is defined as a nuclear reaction in which a heavy nucleus, such as uranium or plutonium, splits into two or more smaller, comparable lighter nuclei accompanied by the release of a massive amount of energy and typically a few neutrons. 
When a thermal neutron is absorbed by a uranium

Question 3

Write down three salient features of nuclear forces that distinguish them from electrostatic and gravitational forces.

Accepted Answer

Nuclear forces are the powerful forces responsible for binding protons and neutrons together inside the atomic nucleus. Their three primary salient features are: Short Range: Nuclear forces are strictly short-range forces. They operate effectively only over very short distances, typically of the ord

Question 4

The half-life of a radioactive substance is 30 days. Calculate the time taken for $7/8^{	ext{th}}$ of the original mass of the substance to disintegrate.

Accepted Answer

Given data: Half-life ($T{1/2}$) = 30 days Fraction disintegrated = $\frac{7}{8}$ 
Step 1: Find the fraction of the substance remaining undecayed ($N$):
Remaining fraction $\frac{N}{N0} = 1 - \frac{7}{8} = \frac{1}{8}$ 
Step 2: Relate the remaining fraction to the number of half-lives ($n$):
We

Question 5

State the radioactive decay law. Derive mathematically the exponential decay law expression $N(t) = N0 e^{-\lambda t}$ for a radioactive substance.

Accepted Answer

Statement of Radioactive Decay Law:
At any instant, the rate of decay of radioactive nuclei (i.e., the number of nuclei decaying per unit time) is directly proportional to the number of undecayed radioactive nuclei present at that instant. Derivation:
Let $N$ be the number of undecayed radioactive

Nuclei