A radioactive isotope has a decay constant of 10-5s4. Calculate half life

Analyze the question

The question appears to have typos. "10-5s4" most likely means a decay constant of λ = 10⁻⁵ s⁻¹. We are asked to find the half-life.

Concept

For radioactive decay, the half-life T½ and decay constant λ are related by:

T½ = ln 2 / λ = 0.693 / λ

Solution

T½ = 0.693 / 10⁻⁵

T½ = 0.693 × 10⁵ s

T½ = 6.93 × 10⁴ s

Check against the options

• A. 6.93 × 10⁻⁵ s: too small
• B. 6.93 × 10⁵ s: this is 10 times too large
• C. 6.93 × 10⁴ s: matches our result
• D. 6.93 × 10⁻⁴ s: too small

Tip

Be careful with the powers of 10 here. Dividing by 10⁻⁵ is the same as multiplying by 10⁵. The 0.693 then has to be written as 6.93 × 10⁻¹, which brings the final power down to 10⁴. A lot of students pick B because they forget to convert 0.693 into standard form. Also remember that a small decay constant means a long half-life.