Problem 58 - Chemistry: An Atoms-Focused Approach

Question

Potassium- 40 decays by three pathways: \(\beta\) decay, positron emission, and electron capture. Write balanced equations for each of these processes.

Step-by-Step Solution

Answer

Question: Write balanced nuclear equations for the three decay pathways of Potassium-40: beta decay, positron emission, and electron capture. Answer: 1. Beta Decay: $^{40}_{19}K \rightarrow ^{40}_{20}Ca + ^0_{-1}e$ 2. Positron Emission: $^{40}_{19}K \rightarrow ^{40}_{18}Ar + ^0_{1}e$ 3. Electron Capture: $^{40}_{19}K + ^0_{-1}e \rightarrow ^{40}_{18}Ar$

Step 1: 1. Beta Decay (β-)

For beta decay, a neutron is converted into a proton, and an electron (beta particle) is emitted. The mass number (A) stays the same, but the atomic number (Z) increases by 1. The equation for this process is: $$ ^{40}_{19}K \rightarrow ^{40}_{20}Ca + ^0_{-1}e $$

Step 2: 2. Positron Emission (β+)

In positron emission, a proton is converted into a neutron, and a positron is emitted. The mass number (A) stays the same, but the atomic number (Z) decreases by 1. The equation for this process is: $$ ^{40}_{19}K \rightarrow ^{40}_{18}Ar + ^0_{1}e $$

Step 3: 3. Electron Capture

In electron capture, a proton captures an electron from the inner shell of the atom, converting it into a neutron. The atomic number (Z) decreases by 1, and the mass number (A) remains the same. The equation for this process is: $$ ^{40}_{19}K + ^0_{-1}e \rightarrow ^{40}_{18}Ar $$