The problem states that the radioactive element decayed to (1)/(8) of its original atoms. This means the fraction remaining (N/N₀) is (1)/(8).

The problem states that the radioactive element decayed to $\frac{1}{8}$ of its original atoms. This means the fraction remaining ($N/N_0$) is $\frac{1}{8}$.

The formula for radioactive decay is:

Substitute the given fraction:

Since $2^3 = 8$, we can write $\frac{1}{8}$ as $\left(\frac{1}{2}\right)^3$.

Therefore, the number of half-lives ($n$) is 3.

The total time elapsed ($t$) is given as 6 minutes. The relationship between total time, number of half-lives, and half-life period is:

Substitute the known values:

Now, solve for $T_{1/2}$:

The final answer is $\text{2 minutes}$.