"you are dating moon rocks based on their proportions of uranium-238 (half-life of about 4.5 billion years) and its ultimate decay product, lead. find the age for each of the following."a. a rock for which you determine that 59 % of the original uranium-238 remains, while the other 41 % has decayed into lead. b. a rock for which you determine that 65 % of the original uranium-238 remains, while the other 35 % has decayed into lead.

Step-by-step explanation:

a.

Initial mass of the isotope = x

Time taken by the sample to decay its mass by 41% = t

Formula used :

where,

= initial mass of isotope  = x

N = mass of the parent isotope left after the time, (t)  = 59% of x = 0.59x

= half life of the isotope  = 4.5 billion years

= rate constant

Now put all the given values in this formula, we get

t = 3.4 billion years

The age a rock is 3.4 billion years.

b.

Initial mass of the isotope = x

Time taken by the sample to decay its mass by 35%= t

Formula used :

where,

= initial mass of isotope  = x

N = mass of the parent isotope left after the time, (t)  = 65% of x = 0.65x

= half life of the isotope  = 4.5 billion years

= rate constant

Now put all the given values in this formula, we get

t = 2.8 billion years

The age a rock is 2.8 billion years.

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step-by-step explanation: