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Systems of Particles and Rotational Motion

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Question : 2 of 33
Marks: +1, -0
In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27A˚(1A˚=1010m)1.27 \text{Å} (1 \text{Å} = 10^{-10}\,\text{m}). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
Solution:  
Let C.M. be at a distance x Å from H-atom
Distance of C.M. from Cl atom =(1.27x)A˚= (1.27 - x) \text{\AA}
Let the mass of H-atom = m units
The mass of the Cl-atom = 35.5 m units
If C.M. is taken at the origin, then
mx+(1.27x)35.5m=0mx + (1.27 - x) 35.5 m = 0
mx=(1.27x)35.5mmx = - (1.27 - x) 35.5 m
Negative sign indicatesthat if Cl atom is on the right side of C.M.(+), the hydrogen atom is on the left side of C.M. So, avoiding, if we get
x+35.5x=1.27×35.5x + 35.5x = 1.27 \times 35.5
36.5x=45.08536.5x = 45.085
x=45.00536.5=1.235A˚x = \frac{45.005}{36.5} = 1.235 \text{\AA}
Therefore, the centre of mass located on theline joining H and Cl nuclei at a distance of 1.24 Å from the H atom.
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