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Bohr's Model of an Atom

In the HCl mo...

Question

In the HCl molecule, separation between the nuclei of two atoms is about $1.46 \circ A$ . Mass of chlorine atom is about $35.5$ times as massive as hydrogen atom and nearly all mass is concentrated at its nucleus. The distance of centre of mass from hydrogen atom is

A

0.67 \circ A

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B

0.73 \circ A

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C

1.42 \circ A

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D

0.96 \circ A

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Solution

The correct option is C $1.42 \circ A$

Position of centre of mass from origin
$X_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}} = \frac{m_{1} (0) + m_{2} (d)}{m_{1} + m_{2}}$
$∵ m_{2} = 35.5 m_{1}$
$∴ X_{c m} = \frac{35.5 \times 1.46}{(35.5 + 1)}$
$X_{c m} = 1.42 \circ A$

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