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# A Radioactive Nucleus Has a Decay Constant λ = 0.3465 (Day)–1. How Long Would It Take the Nucleus to Decay to 75% of Its Initial Amount? - Physics

#### Question

A radioactive nucleus has a decay constant λ = 0.3465 (day)–1. How long would it take the nucleus to decay to 75% of its initial amount?

#### Solution

According to the decay law, we have:

$R = R_0 e^{- \lambda t}$

$\Rightarrow \frac{R_0 \times 75}{100} = R_0 e^{- 0 . 3465t}$

$\Rightarrow \frac{4}{3} = e^{0 . 3465t}$

$\therefore t = 0 . 823 \text { days }$

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Solution A Radioactive Nucleus Has a Decay Constant λ = 0.3465 (Day)–1. How Long Would It Take the Nucleus to Decay to 75% of Its Initial Amount? Concept: Radioactivity - Introduction of Radioactivity.
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