To solve the question about the velocity of \(\alpha\)-rays, let’s start with some fundamental concepts.
### Understanding \(\alpha\)-Rays
\(\alpha\)-rays, or alpha particles, are composed of two protons and two neutrons, making them equivalent to a helium nucleus. They are relatively heavy and positively charged compared to other types of radiation such as beta particles and gamma rays.
### Velocity of \(\alpha\)-Rays
The velocity of \(\alpha\)-rays is significantly less than the velocity of light. This is due to their relatively large mass.
To quantify:
- **Velocity of Light (\(c\))**: Approximately \(3 \times 10^8\) meters per second.
- **Velocity of \(\alpha\)-Rays**: Typically ranges between \(1 \times 10^7\) to \(1 \times 10^8\) meters per second.
From these values:
- The velocity of \(\alpha\)-rays is roughly between \( \frac{1}{10} \)th to \( \frac{1}{3} \)rd of the velocity of light, depending on their energy.
### Answer Analysis
Given the options:
(a) Equal to the velocity of light
(b) \(\frac{1}{10}\)th of the velocity of light
(c) 10 times more than the velocity of light
(d) None of these
**Option (b)** is the closest to the actual velocity range of \(\alpha\)-rays. They are approximately \( \frac{1}{10} \)th of the velocity of light.
**Therefore, the correct answer is (b): \(\frac{1}{10}\)th of the velocity of light.**