215k views
5 votes
The half-life of a 100 gram of Au-198 is 2.3 days. (a) Find the decay constant k. (Write the answer in the exact form or in 5 decimal places)

User Orangutech
by
8.3k points

1 Answer

7 votes

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.

User Aseidma
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories