In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10-10 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.

Asked by Pragya Singh | 1 year ago |  129

#### 1 Answer

##### Solution :-

Given,

Given

mass of hydrogen atom = 1 unit

mass of chlorine atom = 35.5 unit

( As a chlorine atom is 35.5 times the size )

Let the center of mass lie at a distance  x from the chlorine atom

Thus, the distance of center of mass from the hydrogen atom = 1.27 – x

Assuming that the center of mass of HCL lies at the origin,

Hydrogen will lie on the left side of the origin and chlorine lie on the right side of the origin

x =$$\dfrac{ (-m(1.27 -x) + 35.5mx)}{(m + 35.5m)}$$ = 0

-m( 1.27 – x) + 35.5mx = 0

-1.27+x+35.5x = 0

36.5x = 1.27

Therefore, x = $$\dfrac{1.27}{36.5}$$

= 0.035 Å

The center of mass lies at 0.035 Å from the chlorine atom.

Answered by Abhisek | 1 year ago

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