To solve the question, we need to analyze each statement provided in the options to determine which one is true. Let's go through each option step by step.
### Step 1: Analyze Statement A
**Statement A:** Radiant energy is propagated as a wave motion.
- **Explanation:** Radiant energy, which is a form of energy that travels through space, is indeed propagated in the form of electromagnetic waves. This is consistent with the principles of radiation, where heat transfer occurs without the need for a medium. Therefore, Statement A is **true**.
### Step 2: Analyze Statement B
**Statement B:** Positrons have the same mass as that of electrons.
- **Explanation:** A positron is the antiparticle of an electron. Both have the same mass, which is approximately \(9.1 \times 10^{-31} \text{ kg}\), but they have opposite charges (+1 for positron and -1 for electron). Therefore, Statement B is **true**.
### Step 3: Analyze Statement C
**Statement C:** When a nucleus emits a beta particle, its mass number remains unchanged.
- **Explanation:** In beta decay, a nucleus emits a beta particle (which can be an electron or a positron). The emission of a beta particle does not change the mass number of the nucleus, as the mass number is determined by the total number of protons and neutrons. The atomic number may change, but the mass number remains the same. Therefore, Statement C is **true**.
### Step 4: Analyze Statement D
**Statement D:** All the given statements are correct.
- **Explanation:** Since we have established that Statements A, B, and C are all true, it follows that Statement D, which claims that all previous statements are correct, is also **true**.
### Conclusion
After analyzing all the statements, we conclude that all statements A, B, C, and D are correct. Therefore, the correct answer to the question is:
**Option D: All the given statements are correct.**
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