An atom is 40.08 times as heavier as 1/12 mass of an atom of `Cl_2`. What is its atomic mass ?

Answer

To find the atomic mass of the given atom, we can follow these steps:

### Step 1: Determine the atomic mass of chlorine (Cl)
The atomic mass of chlorine (Cl) is given as 35.5 atomic mass units (a.m.u).

### Step 2: Calculate 1/12 of the mass of a chlorine molecule (Cl₂)
Since Cl₂ consists of two chlorine atoms, the molecular mass of Cl₂ is:
\[ \text{Molecular mass of } Cl_2 = 2 \times 35.5 \, \text{a.m.u} = 71 \, \text{a.m.u} \]
Now, we find 1/12 of the mass of Cl₂:
\[ \frac{1}{12} \text{ mass of } Cl_2 = \frac{71}{12} \, \text{a.m.u} \]

### Step 3: Relate the given atom's mass to the calculated value
According to the problem, the mass of the given atom is 40.08 times as heavy as 1/12 of the mass of Cl₂:
\[ \text{Mass of the given atom} = 40.08 \times \frac{71}{12} \, \text{a.m.u} \]

### Step 4: Calculate the mass of the given atom
First, calculate \( \frac{71}{12} \):
\[ \frac{71}{12} \approx 5.9167 \, \text{a.m.u} \]
Now, multiply this by 40.08:
\[ \text{Mass of the given atom} = 40.08 \times 5.9167 \approx 237.75 \, \text{a.m.u} \]

### Step 5: Final Calculation
To find the atomic mass of the given atom, we can simplify our calculation:
\[ \text{Mass of the given atom} = 40.08 \times 5.9167 \approx 237.75 \, \text{a.m.u} \]

Thus, the atomic mass of the given atom is approximately **237.75 a.m.u**.