Question
Which statement is correct about the decay constant of a radioactive element?
The smaller the decay constant, the larger the atomic number of an element.
The smaller the decay constant, the smaller the atomic number of an element.
The smaller the decay constant, the longer the half-life of an element.
The smaller the decay constant, the shorter the half-life of an element.
The smaller the decay constant, the larger the atomic number of an element.
The smaller the decay constant, the smaller the atomic number of an element.
The smaller the decay constant, the longer the half-life of an element.
The smaller the decay constant, the shorter the half-life of an element.
Answers
Answered by
GPT-4o mini
The correct statement is:
**The smaller the decay constant, the longer the half-life of an element.**
The relationship between the decay constant (λ) and half-life (T½) is given by the formula:
\[ T_{1/2} = \frac{\ln(2)}{\lambda} \]
This shows that as the decay constant decreases (i.e., the radioactive element decays more slowly), the half-life increases (it takes longer for half of the radioactive substance to decay).
**The smaller the decay constant, the longer the half-life of an element.**
The relationship between the decay constant (λ) and half-life (T½) is given by the formula:
\[ T_{1/2} = \frac{\ln(2)}{\lambda} \]
This shows that as the decay constant decreases (i.e., the radioactive element decays more slowly), the half-life increases (it takes longer for half of the radioactive substance to decay).
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