Beta Positive Decay Calculator

Beta positive decay (also known as positron emission) is a type of radioactive decay where a proton in the nucleus of an atom is converted into a neutron, a positron (antimatter particle), and a neutrino. This process reduces the atomic number by one while conserving the mass number.

What is Beta Positive Decay?

Beta positive decay occurs when a proton in the nucleus of an atom transforms into a neutron, releasing a positron and a neutrino. This process is the reverse of beta negative decay, where a neutron becomes a proton.

The key characteristics of beta positive decay include:

Reduces the atomic number by 1 (Z → Z-1)
Mass number remains unchanged (A remains the same)
Releases a positron (e⁺) and a neutrino (νₑ)
Often occurs in proton-rich nuclei

Beta positive decay is less common than beta negative decay but occurs in elements with atomic numbers greater than 40, particularly in the upper regions of the periodic table.

How to Calculate Beta Positive Decay

Calculating beta positive decay involves determining the remaining quantity of a radioactive substance after a certain time period. The key parameters needed are:

Initial quantity (N₀)
Half-life (t₁/₂)
Time elapsed (t)

The calculation follows the same exponential decay formula used for all radioactive processes.

Beta Positive Decay Formula

The remaining quantity (N) of a radioactive substance after time (t) can be calculated using the formula:

N = N₀ × (1/2)^{(t / t₁/₂)}

Where:

N = remaining quantity
N₀ = initial quantity
t = elapsed time
t₁/₂ = half-life of the substance

This formula shows that the quantity of the substance decreases exponentially over time.

Beta Positive Decay Example

Let's calculate the remaining quantity of a radioactive substance with an initial quantity of 100 grams, a half-life of 5 years, and after 15 years.

N = 100 × (1/2)^{(15 / 5)} = 100 × (1/2)³ = 100 × 0.125 = 12.5 grams

After 15 years, only 12.5 grams of the substance remain.

Time (years)	Remaining Quantity (grams)
0	100
5	50
10	25
15	12.5

FAQ

What is the difference between beta positive and beta negative decay?

Beta positive decay involves the conversion of a proton to a neutron, releasing a positron and neutrino. Beta negative decay involves the conversion of a neutron to a proton, releasing an electron and antineutrino. The direction of the atomic number change is opposite in each case.

What are the products of beta positive decay?

The primary products of beta positive decay are a neutron, a positron (e⁺), and a neutrino (νₑ). The positron will quickly annihilate with an electron, producing gamma radiation.

How is beta positive decay used in medicine?

Beta positive decay is used in positron emission tomography (PET) scans, where radioactive tracers are injected into the body to help diagnose medical conditions by detecting metabolic activity.

What elements commonly undergo beta positive decay?

Elements with atomic numbers greater than 40, particularly those in the upper regions of the periodic table, commonly undergo beta positive decay. Examples include potassium-40 and sodium-22.