CBSE Class 12 · 2008 · Modern PhysicsShort Answer

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Distinguish between isotopes and isobars. Give one example for each species. A radioactive isotope has a half-life of 5 years. How long will it take for the activity to reduce to 3.125%?

Answer: Isotopes: same $Z$ ; isobars: same $A$ . $t = 25$ years.

Solution

Isotopes: nuclei with the **same atomic number

Z

** but different mass number

A

(e.g.

_{6}^{12} C

and

_{6}^{13} C

).
Isobars: nuclei with the **same mass number

A

** but different atomic number

Z

(e.g.

_{18}^{40} Ar

and

_{20}^{40} Ca

).
Now

3.125% = \frac{1}{32} = (\frac{1}{2})^{5}

, so 5 half-lives have elapsed:

t = 5 \times T_{1/2} = 5 \times 5 = 25 years .

t = 25 years

CBSE Class 12 Board · 2008 · Subjective

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