1. What fraction of a sample of N-16 remains undecayed after 42.78 seconds?

1/64

Explanation:

From the question given above, the following data were obtained:

Time (t) = 42.78 s

Fraction of N–16 remaining (N/N₀) =?

NOTE:

N₀ => is the original amount.

N => is the amount remaining.

Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:

Time (t) = 42.78 s

Half-life (t½) of N–16 = 7.1 s

Number of half-lives (n) =?

n = t / t½

n = 42.78 / 7.1

n = 6

Thus, 6 half-lives has elapsed.

Finally, we shall determine the fraction of N–16 that remains undecayed. This can be obtained as follow:

Number of half-lives (n) = 6

Fraction of N–16 remaining (N/N₀) =?

N = 1/2ⁿ × N₀

N = 1/2⁶ × N₀

N = 1/64 × N₀

Divide both side by N₀

N/N₀ = 1/64

Therefore, 1/64 of the sample remains undecayed.