Question

What particle (a particle, electron, or positron) is emitted in the following radioactive decays? (a) ${}_{14}^{27}Si$ $\to$ ${}_{13}^{27}Al$; (b) ${}_{92}^{238}U$ $\to$ ${}_{90}^{234}Th$; (c) ${}_{33}^{74}As$ $\to$ ${}_{34}^{74}Se$.

Short answer

(a) Positron, (b) Alpha particle, (c) Electron.

Step-by-step solution

Analyze Decay (a) - Silicon to Aluminum

Examine the decay process ${}_{14}^{27}Si{\to }_{13}^{27}Al$. Here, the atomic number decreases by 1 (from 14 to 13), while the mass number remains the same (27). This indicates a beta-plus decay, where a proton is transformed into a neutron, emitting a positron (${\beta }^{+}$).

Analyze Decay (b) - Uranium to Thorium

For the decay ${}_{92}^{238}U{\to }_{90}^{234}Th$, we note that the atomic number decreases by 2 (from 92 to 90) and the mass number decreases by 4 (from 238 to 234). This is characteristic of an alpha decay process, which emits an alpha particle (${}_2^{4}He$ or simply $\alpha$).

Analyze Decay (c) - Arsenic to Selenium

In the decay ${}_{33}^{74}As{\to }_{34}^{74}Se$, the atomic number increases by 1 (from 33 to 34), while the mass number stays the same (74). This indicates a beta-minus decay, where a neutron converts to a proton, resulting in the emission of an electron (${\beta }^{-}$).

Key concepts

Beta-plus decay

Beta-plus decay is an interesting phenomenon in nuclear physics. During beta-plus decay, a proton in an atomic nucleus turns into a neutron. As a result of this transformation, a positron is emitted along with a neutrino. This type of decay decreases the atomic number by one while keeping the mass number constant.

The term positron refers to a particle similar to an electron but with a positive charge. You might imagine it as the electron’s antimatter counterpart. The process can be represented as follows:

$$p^{+}\to n^0+e^{+}+u_e$$

- **Proton (p⁺)** turns into a **neutron (n⁰)**. - Emission of a **positron (e⁺)** and a **neutrino ($u_e$)** occur.

An example of beta-plus decay is when silicon-27 decays into aluminum-27, as in the exercise mentioned. The change in atomic number (14 to 13) signifies this kind of decay has taken place.

Alpha decay

Alpha decay is one of the most recognized forms of radioactive decay. In this process, the nucleus emits an alpha particle. Alpha particles consist of two protons and two neutrons - essentially a helium-4 nucleus. This emission results in a decrease of the atomic number by 2 and the mass number by 4.

The general equation for alpha decay can be presented as:
$$A_X^Z\to A-4_Y^{Z-2}+{}_2^{4}He$$

- Atomic mass **reduces by 4**. - Atomic number **reduces by 2**.
- **Emission of an alpha particle (${}_2^{4}He$)** occurs.

A classic example is the decay of uranium-238 transforming into thorium-234. This shift in both atomic and mass numbers signifies alpha decay. Alpha particles are relatively large and carry a positive charge, thus making them less penetrating but still hazardous to living tissues when ingested or inhaled.

Beta-minus decay

Beta-minus decay adds another fascinating layer to radioactive transformations. In this mode of decay, a neutron within the nucleus converts to a proton, thereby emitting an electron and an antineutrino. This transformation results in an increase in the atomic number by 1, with the mass number remaining unaltered.

The decay process can be denoted as:
$$n^0\to p^{+}+e^{-}+{\bar{u}}_e$$

- **Neutron (n⁰)** is transformed into a **proton (p⁺)**. - Emission of an **electron (e⁻)** and an **antineutrino (${\bar{u}}_e$)** occurs.

An instance from the exercises is arsenic-74 decaying into selenium-74. The rise in the atomic number from 33 to 34 is a key indicator that beta-minus decay has occurred. This type of decay plays a significant role in the stability and transformation of unstable isotopes.