Group Displacement Law

Group displacement law

Fajan, Russel and Soddy (1913) gave group displacement law which states that on the emission of an $\alpha$-particle the new element lies two columns left in the periodic table and mass number decreases by 4 units, and on the emission of a $\beta$-particle the new element lies one column right in the periodic table and mass number remains the same. For example:

$^{226}_{88} Ra \overset{-\alpha}{\rightarrow} ^{222}_{86}Rn \; \; ^{214}_{84}Po \overset{-\alpha}{\rightarrow} ^{210}_{82}Pb \\[3mm] \text{II Gp.} \; \; \; \; 0 \; \; \; \; \text{VI Gp.} \; \; \; \; \text{IV Gp.} \\[3mm] ^{24}_{11}Na \overset{-\beta}{\rightarrow} ^{24}_{12} Mg \; \; ^{210}_{82}Pb\overset{-\beta}{\rightarrow}^{210}_{83}Bi \\[3mm] \text{I Gp.} \; \; \; \; \text{II Gp.} \; \; \; \; \text{IV Gp.} \; \; \; \; \text{V Gp.}$

Remember this law is not valid for lanthanides (at. No. 58 to 71), actinides (at. No. 90 to 103) and elements of VIII group. Due to the presence of many elements in the same period of the same group.

To find number of a, b particles:

Number of a-particles = $\dfrac{\text{change in mass no.}}{4}$

Number of b-particles = $2 \times \alpha-\text{particles}- [Z_1-Z_2]$

Ex. $^{238}_{92}U \to ^{206}_{82} Pb$

Number of $\alpha$-particles = $\dfrac{238- 206}{4} = 8$

Number of $\beta$-particles = $2 \times 8- [92- 82] = 6$

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