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Nuclear decay occurs according to first-order kinetics. Scandium-43 decays with a rate constant of 0. 178 days–1. After 15. 0 days, a sample has a mass of 1. 73 g. What was the original mass of the sample?.

Respuesta :

KunalYadav273

The original weight of the specimen is 25.0 g since, according to the question, nuclear decay follows first-order kinetics.

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Briefing:

Given:

r = 0.178 days⁻¹

[tex]N_{t}[/tex] = 1.73 g

[tex]N_{o}[/tex] = ?

[tex]t_{1/2}[/tex] = 0.693/λ

Therefore,

ln[tex]N_{t}[/tex]/[tex]N_{0}[/tex] = -λt

[tex]N_{t}[/tex] = [tex]N_{0}[/tex]e⁻λt

    = (1.73)e(-0.131y⁻¹)(30y)

    = 25.0 g

Consequently, the sample's starting mass is 25.0 g.

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