a chunk of basalt has been analyzed using the k40 to ar40 radio decay m. after analysis it was determined…

Explanation:

Step1: Calculate initial amount of K - 40

The amount of Ar - 40 is formed from the decay of K - 40. The initial amount of K - 40 ($N_0$) is the sum of the remaining K - 40 ($N$) and the amount of K - 40 that decayed to form Ar - 40. Since the amount of Ar - 40 is 155g and remaining K - 40 is 5g, $N_0=155 + 5=160$g.

Step2: Determine number of half - lives ($n$)

The formula for radioactive decay is $N = N_0(\frac{1}{2})^n$. We know $N = 5$g and $N_0 = 160$g. Substituting these values into the formula gives $5=160(\frac{1}{2})^n$. Then $\frac{5}{160}=(\frac{1}{2})^n$, and $\frac{1}{32}=(\frac{1}{2})^n$. Since $\frac{1}{32}=(\frac{1}{2})^5$, $n = 5$.

Step3: Calculate age of the sample ($t$)

The half - life ($T_{1/2}$) is $1.3\times10^9$ years. The age of the sample $t=n\times T_{1/2}$. Substituting $n = 5$ and $T_{1/2}=1.3\times10^9$ years, we get $t = 5\times1.3\times10^9=6.5\times10^9$ years or 6.5 billion years.

Answer:

6.5 billion years