Consider alpha-particles, beta-particles and gamma-rays each having an energy of 0.5 MeV. In increas

Q: Why do alpha particles have the lowest penetrating power despite being the heaviest?

Their large mass makes them very slow for a given kinetic energy. Combined with their $+2e$ charge, they interact strongly with the electrons of the material they pass through, losing their energy very quickly over a short distance.

Q: Does the energy of 0.5 MeV change the standard order of penetration?

No, 0.5 MeV is a typical energy scale for nuclear decays. At this energy, the relative velocities and interaction cross-sections still dictate that $\gamma > \beta > \alpha$ in terms of penetration.

Q: What exactly is a beta particle?

A beta particle is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus.

Q: Why are gamma rays so penetrating?

Gamma rays are electromagnetic waves (photons) with no rest mass and no electric charge. They don't experience Coulomb forces from nuclei or electrons, so they only lose energy through direct collisions, which are rare.

Q: Is the answer key in the book correct?

The book's answer key states option (d), which is $\gamma, \beta, \alpha$. However, the question asks for the *increasing* order of penetrating power. Since $\alpha$ has the least and $\gamma$ has the most, the correct increasing order is $\alpha, \beta, \gamma$, which corresponds to option (a). The book's solution text actually supports option (a).

Question

Consider $\alpha$-particles, $\beta$-particles and $\gamma$-rays each having an energy of $0.5	ext{ MeV}$. In increasing order of penetrating powers, the radiations are

Options:

(A) $\alpha, \beta, \gamma$

(B) $\alpha, \gamma, \beta$

(C) $\beta, \gamma, \alpha$

(D) $\gamma, \beta, \alpha$

Sigma Percentile · Accepted Answer

### The Nature of Radioactive Emissions

To understand how different types of radiation interact with matter, we must first look at their fundamental properties. Radioactive decay typically produces three main types of emissions: $\alpha$-particles, $\beta$-particles, and $\gamma$-rays.

An **$\alpha$-particle** is essentially a helium nucleus ($^4_2	ext{He}$). It is massive (about $4	ext{ amu}$) and carries a strong positive charge of $+2e$.

A **$\beta$-particle** is a high-speed electron ejected from the nucleus. It is extremely light (about $\frac{1}{1836}	ext{ amu}$) and carries a negative charge of $-1e$.

A **$\gamma$-ray** is not a particle in the traditional sense, but a high-energy photon of electromagnetic radiation. It has zero rest mass and zero electric charge.

### The Role of Velocity and Ionization

The problem states that all three radiations have the exact same kinetic energy: $0.5	ext{ MeV}$. Since kinetic energy is given by $K = \frac{1}{2}mv^2$ (for non-relativistic speeds), the velocity of a particle is inversely related to its mass.

Because the $\alpha$-particle is by far the heaviest, it will travel the slowest. The $\beta$-particle, being much lighter, will travel at a significant fraction of the speed of light. The $\gamma$-ray, being a massless photon, always travels exactly at the speed of light, $c$.

When these radiations pass through a material, they interact with the atoms inside it, knocking off electrons and causing **ionization**. The ionizing power of a radiation depends on two main factors: its charge and the time it spends near an atom.

Because the $\alpha$-particle is slow-moving and has a large $+2e$ charge, it exerts a strong electromagnetic force on nearby electrons for a relatively long time. This makes it highly ionizing. Conversely, the $\gamma$-ray, with no charge and moving at the speed of light, rarely interacts with atoms, making it the least ionizing.

### Penetrating Power: The Inverse of Ionization

Every time a radiation particle ionizes an atom, it loses a fraction of its kinetic energy. Therefore, a particle with high ionizing power will lose its energy very quickly and come to a halt over a very short distance.

This leads to a fundamental rule of thumb in nuclear physics: **Penetrating power is inversely proportional to ionizing power.**

- **$\alpha$-particles** ionize heavily and lose their $0.5	ext{ MeV}$ of energy almost immediately. They can be stopped by a simple sheet of paper or even a few centimeters of air.
- **$\beta$-particles** ionize less frequently. They can pass through paper but will be stopped by a thin sheet of aluminum.
- **$\gamma$-rays** rarely ionize atoms. They can travel through paper, aluminum, and even human tissue with ease, requiring several centimeters of dense lead to be significantly attenuated.

Therefore, the order of penetrating power from weakest to strongest is $\alpha < \beta < \gamma$. The correct increasing order is $\alpha, \beta, \gamma$.

*(Note: Some older textbooks or answer keys mistakenly list the decreasing order or contain typographical errors for this specific question. The physics, however, unequivocally dictates that $\alpha$ is the least penetrating and $\gamma$ is the most penetrating.)*

Animated Solution for Physics - Atoms and Nuclei: Consider $α$ -particles, $β$ -particles and $γ$ -rays each having an energy of $0.5 MeV$ . In increasing order of penetrating powers, the radiations are

Select Answer:

Visualized Solution

$Understanding the Particles$

$Velocity Comparison$

$Ionizing Power$

$Penetrating Power$

$Final Order$

The Sigma Insight: Radioactivity

The Nature of Radioactive Emissions

The Role of Velocity and Ionization

Penetrating Power

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