Question

what is the half-life of a radioactive substance that decays at a continuous rate of 11% per minute? (round to one decimal places.)

Answer 1

5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

Define the half-life of a radioactive substance?

• A radioactive sample's half-life is the amount of time it takes for half of its atomic nuclei to spontaneously transform into another nuclear species and emit particles and energy.

When we use the formula A = A0(1 - r)t,

• where A is the quantity of a substance we have at any given moment (t),
• A₀ is the quantity we have at the beginning (at t = 0), and
• r is the rate of decay, we may state the following:

(1/2)A₀ = A₀(1 - 0.11)t

[Divide both sides by A₀ results in:

1/2 = (0.87)t

Using the log of both sides;:

log(1/2) = log(0.87)t

Using a logarithm property, we can bring the "t" to the front, giving us:

log(1/2) = t.log(0.89)

[Dividing both sides with log(0.89) gets us:

t =  log(1/2)/log(0.89)

Using calculator for soling the values.

t = 5.94 seconds

Thus, 5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

To know more about the half-life of a radioactive substance, here

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