`alpha`-particles and `gamma`-rays are all having same energy . Their penetrating power in a given medium in increasing order will be

Options

A. `beta , gamma , alpha`
B. `gamma , alpha , beta`
C. `alpha , beta , gamma`
D. `beta , alpha , gamma`

Explanation

To determine the penetrating power of alpha particles and gamma rays in a given medium when they all have the same energy, we can analyze the properties of each type of radiation:

### Step-by-Step Solution:

1. **Identify the Types of Radiation**:
- Alpha particles (α): These are helium nuclei consisting of 2 protons and 2 neutrons. They are relatively heavy and positively charged.
- Beta particles (β): These are electrons (or positrons) emitted from a nucleus during radioactive decay. They are much lighter than alpha particles and have a negative charge (for electrons).
- Gamma rays (γ): These are high-energy photons (electromagnetic radiation) that have no mass and no charge.

2. **Understand Penetrating Power**:
- Penetrating power refers to the ability of radiation to pass through a material. It depends on the mass, charge, and energy of the particles.
- Heavier and charged particles (like alpha particles) interact more with matter and lose energy quickly, resulting in lower penetrating power.
- Light and uncharged particles (like gamma rays) can penetrate materials more effectively.

3. **Compare the Penetrating Powers**:
- **Alpha Particles**: Due to their large mass and positive charge, alpha particles have the least penetrating power. They can be stopped by a sheet of paper or even the outer layer of human skin.
- **Beta Particles**: Being lighter and negatively charged, beta particles have greater penetrating power than alpha particles. They can penetrate through paper but are stopped by materials like plastic or aluminum.
- **Gamma Rays**: Gamma rays, being massless and uncharged, have the highest penetrating power. They can pass through several centimeters of lead or concrete.

4. **Order the Penetrating Powers**:
- Based on the analysis, we can arrange the penetrating powers in increasing order:
- Alpha particles (least penetrating)
- Beta particles
- Gamma rays (most penetrating)

5. **Final Answer**:
- The penetrating power in increasing order is:
- Alpha particles < Beta particles < Gamma rays.