# Radioactive Equilibrium

**Radioactive Equilibrium**

In radioactive transformation when a daughter element transforms at the same rate at which it is formed from the parent element that state is known as radioactive equilibrium e.g.

parent intermediate daughter

*At equilibrium*

Or,

**Example 1**: disintegrates to give as the final product. How many alpha and beta particles are emitted during this process?

Solution: in this process change in at. Wt. =234 – 206 = 28 a.m.u. since by the emission of one -particle m. no. decreases by 4 units hence no. of emitted -particle = 28/4 = 7

If only -particles emit then the at. No. of the product should be 90 – 2 × 7 = 76.

But here the at. no. of the product is 82 that is due to the eimission of -particles and its no. is 82 – 76 = 6

**Example 2**: The activity of a radio isotope falls to 12.5% in 90 days. Compute the half life and decay constant of the radio isotope.

Solution:

Since,

**Example 3: **Calculate the weight in gram of 1 curie and 1rd of

Solution:

From eq. 3

Total no. of atoms in w gram

From eq. 1,

According to definition of curie

According to definition of Rutherford

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