The distance between the hydrogen atom and the fluorine atom in a hydrogen fluoride (HF) is 0.92 Armstrong. the mass of hydrogen atom is 1 a.m.u and mass of fluorine atom is 19 a.m.u the position of the centre of mass of the hydrogen fluoride molecule is

Options

A. 0.5 Armstrong from hydrogen atom
B. 0.5 Armstrong from fluorine atom
C. 0.87 Armstrong from hydrogen atom
D. 0.87 Armstrong from fluorine atom

Answer

To find the position of the center of mass of the hydrogen fluoride (HF) molecule, we can use the formula for the center of mass (CM) of a two-particle system. The formula is given by:

\[ R_{CM} = \frac{m_1 r_1 + m_2 r_2}{m_1 + m_2} \]

Where:
- \(m_1\) is the mass of the first particle (hydrogen),
- \(r_1\) is the position of the first particle,
- \(m_2\) is the mass of the second particle (fluorine),
- \(r_2\) is the position of the second particle.

### Step 1: Assign values to the variables
- Mass of hydrogen (\(m_1\)) = 1 a.m.u
- Mass of fluorine (\(m_2\)) = 19 a.m.u
- Distance between hydrogen and fluorine = 0.92 Å
- We can assume the position of the hydrogen atom (\(r_1\)) to be at 0 Å (origin) and the position of the fluorine atom (\(r_2\)) to be at 0.92 Å.

### Step 2: Substitute the values into the CM formula
Now, we can substitute the values into the center of mass formula:

\[ R_{CM} = \frac{(1 \, \text{a.m.u}) \cdot (0 \, \text{Å}) + (19 \, \text{a.m.u}) \cdot (0.92 \, \text{Å})}{1 \, \text{a.m.u} + 19 \, \text{a.m.u}} \]

### Step 3: Calculate the numerator and denominator
- Numerator:
\[ (1 \cdot 0) + (19 \cdot 0.92) = 0 + 17.48 = 17.48 \, \text{a.m.u} \cdot \text{Å} \]
- Denominator:
\[ 1 + 19 = 20 \, \text{a.m.u} \]

### Step 4: Calculate the center of mass
Now, we can calculate \(R_{CM}\):

\[ R_{CM} = \frac{17.48 \, \text{a.m.u} \cdot \text{Å}}{20 \, \text{a.m.u}} = 0.874 \, \text{Å} \]

### Step 5: Interpret the result
The center of mass is located approximately 0.87 Å from the hydrogen atom.

### Final Answer
The position of the center of mass of the hydrogen fluoride molecule is approximately 0.87 Å from the hydrogen atom.

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