Question

A certain radioactive isotope has a half life of 1100 years. How many years to the nearest year would be required for a given amount of this isotope to decay 30% of that amount.

Answer 1

The number of years it would take for the isotopes to decay to 30% of their original amount is 660 years.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

A certain radioactive isotope has a half-life of 1100 years.

This means that,

The original amount will be 50% after 1100 years.

50% = 50/100 = 0.5

This can be written as,

1100 years = 50% ____(1)

Now,

After 1100 years the amount will be,

50% of 0.5 = 0.5 x 0.5 = 0.25

This means we can write,

(1100 + 1100) years = 0.25

2200 years = 0.25

2200 years = 25% ____(2)

From (1) or (2) we can calculate.

1100 years = 50%

Multiply 30/50 on both sides.

30/50 x 1100 years = 30%

660 years = 30%

Thus,

The number of years it would take for the isotopes to decay to 30% of their original amount is 660 years.

Learn more about percentages here:

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