Question

A newly prepared radioactive nuclide has a decay constant of 6.93 s\(^{-1}\). What is the half-life of the nuclide?

• A. 0.1 s
• B. 0.2 s
• C. 0.3 s
• D. 0.4 s

Hint:

Always remember the formula $t_{1/2} = \frac{0.693}{\lambda}$ when dealing with radioactive decay problems.

Answer 1

The Correct Option is A

The half-life (\(t_{1/2}\)) of a radioactive nuclide is related to the decay constant (\(\lambda\)) by the following formula:

\[ t_{1/2} = \frac{\ln(2)}{\lambda} \]

Where:

• \( t_{1/2} \) is the half-life of the nuclide,
• \( \lambda \) is the decay constant, and
• \( \ln(2) \approx 0.693 \).

Given that the decay constant \( \lambda = 6.93 \, \text{s}^{-1} \), we can substitute this value into the formula:

\[ t_{1/2} = \frac{0.693}{6.93} \]

Now, performing the division:

\[ t_{1/2} \approx 0.1 \, \text{seconds} \]

Final Answer:

The half-life of the nuclide is approximately \( \boxed{0.1} \) seconds.