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After 1 hour, `(1/8)^"th"` of the initial mass of a certain radioactive isotope remains undecayed. The half-life of the isotopes is ______.

#### Options

10 minutes

20 minutes

40 minutes

80 minutes

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#### Solution

After 1 hour, `(1/8)^"th"` of the initial mass of a certain radioactive isotope remains undecayed. The half-life of the isotopes is **20 minutes**.

**Explanation:**

`1/8 = 1/2^3`

` therefore` n = 3

t = 1 hour = 60 minutes

` therefore "T" = "t"/"n" = (60 "minutes")/3`

= 20 minutes

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