Question

In a Dobereiner's triad, the atomic weights of first two elements are x and y. What should be the atomic weight of the $3$rd element?

• A. $\text{x+y}$
• B. $\text{x-y}$
• C. $\text{x+2y}$
• D. $\text{2y-x}$

Answer 1

The correct option is D

$\text{2y-x}$

Explanation for the correct option: (d)

1. According to Dobereiner's law of triads, when the elements are arranged in the increasing order of atomic masses the atomic mass of the central element will be approximately equal to the arithmetic mean of the atomic masses of the other two elements.
2. Here let ‘z’ be the third element whereas ‘x’ and ‘y’ are the first two elements.
3. The atomic weight of $3^{rd}$ element is:

$\begin{array}{rcl}& & \text{y=}\frac{\text{x+z}}{2}\\ & & \text{2y=x+z}\\ & & \text{z=2y-x}\end{array}$

Hence the atomic weight of the third element is $\text{2y-x}$.

Explanation for the incorrect options:

a) In a Dobereiner's triad, if the atomic weights of the first two elements are x and y then the atomic weight of the $3$rd element is $2\text{y-x}$ not $\text{x+y}$.

b) $\text{x-y}$ is not the atomic weight of the third element in a Dobereiner's triad in which the atomic weights of the first two elements are x and y.

c) $2\text{y-x}$ is the atomic weight of the third element in a Dobereiner's triad in which the atomic weights of the first two elements are x and y. $\text{x+2y}$ is not correct.

Hence option (d) is correct and the atomic weight of the third element is $\text{2y-x}$.