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(C) Let the mass of the hydrogen atom be $m_1 = 1$ unit and the mass of the chlorine atom be $m_2 = 35.5$ units.Place the hydrogen atom at the origin

Vedclass · Accepted Answer

$1.24$

Vedclass · Answer

(C) Let the mass of the hydrogen atom be $m_1 = 1$ unit and the mass of the chlorine atom be $m_2 = 35.5$ units.Place the hydrogen atom at the origin $(0, 0)$,so its position is $\vec{r}_1 = 0$.The chlorine atom is at a distance of $1.27 \, \mathring{A}$ along the x-axis,so its position is $\vec{r}_2 = 1.27 \, \hat{i} \, \mathring{A}$.The position of the centre of mass $\vec{R}$ is given by the formula:$\vec{R} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2}{m_1 + m_2}$Substituting the values:$\vec{R} = \frac{1 	imes 0 + 35.5 	imes 1.27 \hat{i}}{1 + 35.5}$$\vec{R} = \frac{35.5 	imes 1.27}{36.5} \hat{i}$$\vec{R} \approx 0.9726 	imes 1.27 \hat{i} \approx 1.24 \hat{i} \, \mathring{A}$.Thus,the centre of mass is located at approximately $1.24 \, \mathring{A}$ from the hydrogen atom.

Column-$I$	Column-$II$
$(1)$ $\frac{{{m_1}{m_2}}}{{{m_1} + {m_2}}}$	$(a)$ Reduced mass of a two-particle system
$(2)$ $\frac{{{r_1} + {r_2}}}{2}$	$(b)$ Position vector of the center of mass for a system of two equal masses

Similar Questions

Match Column-$I$ with Column-$II$.
Column-$I$ Column-$II$
$(1)$ $\frac{{{m_1}{m_2}}}{{{m_1} + {m_2}}}$ $(a)$ Reduced mass of a two-particle system
$(2)$ $\frac{{{r_1} + {r_2}}}{2}$ $(b)$ Position vector of the center of mass for a system of two equal masses

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