A radioactive element has a half-life of 1.6 hours.How many hours will it take for the number of atoms present to decay to one-sixteenth of the initial value?
A)26
B)13
C)6.4
D)0.15
E)16

Question

Quizplus · Accepted Answer

Let's denote the initial number of atoms as N₀. After one half-life, the number of atoms will be N₀/2. After two half-lives, the number of atoms will be N₀/4. We can generalize this pattern as:

Number of atoms after t half-lives = N₀/(2^t)

We want to find the time t for which the number of atoms is 1/16 of the initial value:

N₀/(2^t) = N₀/16

Canceling the N₀ from both sides and simplifying:

2^t = 16
2^t = 2^4
t = 4

Since each half-life is 1.6 hours, four half-lives will be:

4 x 1.6 = 6.4 hours

Therefore, the answer is choice C.

A Radioactive Element Has a Half-Life of 1