The half-life (t₁/₂) of a radioactive isotope can be calculated using the following equation:
t₁/₂ = ln(2) / λ
where:- * t₁/₂ is the half-life in seconds
* ln(2) is the natural logarithm of 2 (approximately 0.693)
* λ is the decay constant in seconds⁻¹
We are given that the decay constant of gallium-67 (⁶⁷Ga) is 0.00886 hours⁻¹.
First, let's convert the decay constant from hours⁻¹ to seconds⁻¹:
* λ = 0.00886 hours⁻¹
* 3600 seconds/hour = 3.2136 x 10⁻³ seconds⁻¹
Now you can plug the decay constant into the equation and solve for the half-life:
t₁/₂ = ln(2) / (3.2136 x 10⁻³) seconds⁻¹ ≈ 2.14 x 10⁵ seconds
I HOPE IT HELPS OR IF ANY CORRECTIONS ARE NEEDED PLEASE INFORM AT THE EARLIEST
