Question

calculate the uranium X1 Decay constant from its half life.how long would it take to decompose 30 percent of the original sample ?

Answer 1

Explanation:

So, the decay constant for Uranium is k = 0.154 × 10⁻⁹ yr⁻¹ and the it would take 2.318 billion years to decompose 30% of the original sample.

Answer 2

Concept:

• Half-lives
• Radioactivity
• Radioactive decay is an example of a first-order reaction
• Chemical kinetics

Given:

• Uranium sample
• 30% of the original sample is decomposed
• The half-life of uranium T1/2 = 4.5* 10^9 years

Find:

• The time it would take for 30% of the original sample to be decomposed

Solution:

For a first-order reaction,

k = 0.693/T1/2

k = 0.693/4.5* 10^9

30% of the sample is decomposed  

0.3 of the sample has decomposed, leaving behind 0.7 of the sample

At/Ao = 0.7

Ao/At = 1/0.7 = 10/7

ln [At] = -kt + ln [Ao]

kt = ln [Ao] - ln [At]

kt = ln [Ao/At]

kt = ln (10/7)

t = 1/k (ln (10/7))

t = 4.5* 10^9/0.693 * (ln (10/7))

t = 2.3 * 10^9 years

It would take 2.3 * 10^9 years.

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