Group displacement law

The scientists named Soddy, Fajans and Russell (during the year1911-1913) observed that when the α-particle is lost, a new element with atomic number less by 2 and mass number less by 4 is obtained. Similarly, the when the  β -particle is lost, a new element with atomic number greater by 1 is obtained. The element emitting then  α or β-particle is called the parent element and the new element formed is called as the daughter element. The results have been summarized as follows,

(1) When an  α -particle is emitted, the new element formed is displaced two positions to the left in the periodic table than that of the parent element (because the atomic number decreases by 2).

(2) When a  β -particle is emitted, the new element formed is displaced one position to the right in the periodic table than that of the parent element (because atomic number increased by 1).

(3) When the positron is emitted, the daughter element takes its position one group to the left of the parent element in periodic table.

The group displacement law should be applied with the great care especially in case of the elements of the lanthanide series (57 to 71), actinide sequence (89 to 103), VIII group (26 to 28; 44 to 46; 76 to 78), IA and IIA groups.

To determine number of α- and  β - particles emitted during nuclear alteration. It can be done in manner shown below, 

a= b+4x or x=a-b/4                         .....(i)

c=d + 2x -y                                           .....(ii)

here x = no. of a-emitted, y = no. of b-emitted

substituting the value of x from equation (i) in equation (ii)
      
        we get ; 

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