A nuclide has a decay constant of 4.28 ×10^-4 h^-1. If the activity of a sample is 3.14 ×10^5 s^

step 1 Okay, so in this question, they tell us that the K constant, lambda, is 4 .28 times 10 to negati

A nuclide has a decay constant of 4.28 ×10^-4 h^-1. If the...

A nuclide has a decay constant of $4.28 \times 10^{-4} \mathrm{h}^{-1}$. If the activity of a sample is $3.14 \times 10^{5} \mathrm{s}^{-1},$ how many atoms of the nuclide are present in the sample? (a) $2.64 \times 10^{12} ;$ (b) $7.34 \times 10^{8}$ (c) $2.04 \times 10^{5}$ (d) $4.40 \times 10^{10} ;$ (e) none of these.

A nuclide has a decay constant of $4.28 \times 10^{-4} \mathrm{h}^{-1}$. If the activity of a sample is $3.14 \times 10^{5} \mathrm{s}^{-1},$ how many atoms of the nuclide are present in the sample?
(a) $2.64 \times 10^{12} ;$ (b) $7.34 \times 10^{8}$
(c) $2.04 \times 10^{5}$
(d) $4.40 \times 10^{10} ;$ (e) none of these.

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Key Concepts

Decay Constant

The decay constant represents the probability per unit time that a given nucleus will decay. It is a fundamental parameter in radioactive decay calculations and is used to determine how quickly a radioactive substance decreases, regardless of the type of nuclide.

Exponential Decay Relationship

The exponential decay relationship, expressed by the equation A = ?N, directly relates the activity (A) of a radioactive sample to the decay constant (?) and the number of radioactive atoms (N). This equation helps in calculating any one of these variables if the other two are known.

Activity

Activity is the rate at which radioactive nuclei decay, typically measured in disintegrations per second (Becquerels). It quantifies the number of decays occurring in a sample per unit time and is directly proportional to the number of radioactive atoms present.

Unit Conversion

Unit conversion is essential when variables are expressed in different time units. In radioactive decay problems, it is common to convert the decay constant from one time unit (such as hours) to another (such as seconds) to ensure consistency within the calculation using the exponential decay formula.

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