# The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be a. 2/3√2 b. ½ c. 1/2√2 d. ⅔

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Updated on: September 13th, 2023

The half-life of a radioactive nuclide is defined as the time in which half of the original number of radioactive atoms has decayed.

Given

TH = 150 hours

t/2 = 100 hours

Table of content

We know that the activity of a radioactive substance is written as

A = Ao (1/2)TH/t/2

Where TH is the fraction of the original activity

t/2 is the half-life of a radioactive nuclide

Substituting the values

A/Ao = (1/2)150/100

By further simplification

A/Ao = (1/2)3/2

So we get

A/Ao = 1/2√2

Therefore, the fraction of original activity that will remain after 150 hours would be 1/2√2.

Summary:

4. ## ⅔

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be 1/2√2.

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