The correct option for the question regarding the particles emitted when \(^{39}_{19}K\) (potassium-39) decays to \(^{39}_{19}K\) is **A. gamma**. ### Explanation of the Correct Answer 1. **Understanding the Decay Process**: - The notation \(^{39}_{19}K\) indicates that we are dealing with potassium-39, which has 19 protons and 20 neutrons (39 - 19 = 20). - The question states that potassium-39 decays to potassium-39. This means that there is no change in the atomic number (19) or the mass number (39). 2. **Types of Decay**: - **Alpha Decay**: This involves the emission of an alpha particle (2 protons and 2 neutrons). This would change the element to a different one (e.g., from potassium to argon). - **Beta Decay**: This involves the emission of a beta particle (an electron or positron) and also changes the element (e.g., from potassium to calcium). - **Gamma Decay**: This involves the emission of gamma radiation, which is a form of electromagnetic radiation. Gamma decay does not change the atomic number or mass number of the nucleus; it simply releases energy from the nucleus. - **Electron Emission**: This is essentially the same as beta decay, where an electron is emitted, leading to a change in the element. 3. **Why Gamma Decay is the Correct Answer**: - Since the decay process described does not change the identity of the element (it remains potassium-39), the only type of decay that fits this description is gamma decay. Gamma radiation is emitted when a nucleus transitions from a higher energy state to a lower energy state without changing its composition. ### Why the Other Options are Incorrect - **B. Beta**: Beta decay involves the transformation of a neutron into a proton (or vice versa) and the emission of a beta particle (electron or positron). This would change the element from potassium-39 to another element (like calcium-39 or argon-39), which is not the case here. - **C. Electron**: This option is misleading because while beta decay involves the emission of an electron, it also results in a change of the element. Since the decay does not change the element, this option is not applicable. - **D. Alpha**: Alpha decay would result in the emission of an alpha particle, which consists of 2 protons and 2 neutrons. This would change potassium-39 into a different element (argon-35), which again does not match the scenario given in the question. ### Summary of Key Points - **Gamma decay** is the emission of high-energy photons without changing the atomic or mass number. - **Alpha and beta decay** involve changes in the atomic structure and result in different elements. - The decay of \(^{39}_{19}K\) to \(^{39}_{19}K\) indicates no change in the element, confirming gamma decay as the correct answer. ### Revision Summary - **Gamma decay** does not change the element or its mass number. - **Alpha and beta decay** result in the transformation of the element. - The emission of gamma radiation is a common way for excited nuclei to release energy. - Always check if the atomic and mass numbers change to determine the type of decay.