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Fundamentals Of Physics
Found in: Page 1304

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Short Answer

Calculate the mass of a sample of (initially pure) K40 that has an initial decay rate of1.70×105 disintegrations/s. The isotope has a half-life of 1.28×109y.

The mass of a sample of K40 is 0.66g.

See the step by step solution

Step by Step Solution

Step 1: The given data

a) Initial decay rate of K40 ,R0=1.70×105 disintegration/s,

b) Half-life of the isotope, T1/2=1.28×109 or 4.04×1016 s

c) Molar mass of the sample, A=40g/mol

Step 2: Understanding the concept of decay  and mass

The radioactive decay is due to the loss of the elementary particles from an unstable nucleus to convert them into a more stable one. From the concept of the decay rate, we can get the number of undecayed nuclei. Now, using this in the equation of finding the number of nuclei then determine unknown mass of the sample using its molar mass value and Avogadro number.


The rate of decay is as follows:

R=In 2T1/2N ……. (i)

Here, λ is the disintegration constant, N is the number of undecayed nuclei.

T1/2 is the half-life of the substance, the number of atoms in a given mass of an atom.

N=mANAHere , NA=6.022×1023atomsmol …… (ii)

Step 3: Calculate the mass of the potassium sample

Substituting value of number of undecayed nuclei from the equation (i) in equation (ii), determine the mass of the potassium sample as follows:

m=RT1/2In 2ANA

Substitute the values and solve as:

m=1.70×105disintegrations4.04×1016sIn 240gmol6.022×1023atomsmol =0.66 g

Hence, the value of the mass is 0.66g.

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