Question

If the distance between the centers of the atoms of potassium and bromine in $\text{KBr}$ (potassium-bromide) molecule is $0.282\times {10}^{-9}m,$ find the centre of mass of this two-particle system from potassium (mass of bromine$=80u,$ and of potassium $=39u$ ).

Answer 1

Let position coordinate of potassium,$X_K=0$

Position co-ordinate of bromine,

$X_{Br}=0.282\times {10}^{-9}m$.

Position co-ordinate of centre of mass-

$X_{CM}=\frac{m_k{X}_k+m_{Br}{X}_{Br}}{m_k+m_{Br}}$

$X_{CM}=\frac{39\times 0+80\times 0.282\times {10}^{-9}}{39+80}$

$=0.189\times {10}^{-9}m$