Final answer:
The decay constant k for Au-198 with a half-life of 2.3 days is calculated using the formula k = ln(2) / t1/2, resulting in a value expressed either in exact form or in five decimal places.
Step-by-step explanation:
To find the decay constant k for Au-198 with a half-life of 2.3 days, we use the formula that relates the decay constant to the half-life:
k = ln(2) / t₁/₂
Where ln(2) is the natural logarithm of 2 (approximately equal to 0.693) and t₁/₂ is the half-life.
Therefore, we have:
k = ln(2) / 2.3 days
This calculation gives us the value of k in days⁻¹. In order to make it more accurate, we'll express the answer in five decimal places if not in exact form.
Note: The unit for time (days) is included to indicate that this is how k should be interpreted when using it in further calculations.