Question

half life of a radioactive element is 6930 years.what is the average life time in years of the element
​

Answer 1

Answer:

Average Life Period & half life period-

Half Life Period-

“It is equal to the time required to disintegrate half of the quantity of the radioactive element taken”.

or

“Half life period is the time during which half of the quantity of a sample of radioactive element disintegrates.”

Half life is represented by t1/2. The value of t1/2 does not depend upon temperature, pressure, catalyst and mass of radioactive substance taken etc.

t1/2 is a measure of radioactivity and stability of radioactive element. Greater is the value of t1/2, greater is the stability of the radioactive element & smaller is its radioactivity.

Ex.- Half life of Ra226 is 1580 years. This shows that after 1580 years, the mass of radium is half of the mass taken.

After 2×1580 (=3160 year) the quantity of Ra226 left will be ¼ ( one fourth) of the mass taken.

Suppose initial mass or no. of atoms of a radioactive element is No. its half life period is t1/2

After one t1/2atoms left = No/2

Atoms left after two half lives = No/4=No/22

After three half lives atoms left= No/8 = No/23

Atoms left after ‘n’ half lives= No/2n

The mass or no. of atoms left after ‘n’ half lives is ‘N’

N= No(1/2)n

T=n×t­1/2