The specific heat of a metal is `0.836 J//g`. The approximate at.wt.is:

Options

A. `16`
B. `64`
C. `40`
D. `32`

Explanation

To find the approximate atomic weight of a metal given its specific heat, we can use the relationship between atomic weight, specific heat, and a constant value. Here’s a step-by-step solution:

### Step 1: Understand the relationship
The relationship we will use is:
\[ \text{Atomic Weight} \times \text{Specific Heat} = 6.4 \]

### Step 2: Identify the specific heat
Given that the specific heat of the metal is \( 0.836 \, \text{J/g} \), we need to convert this to calories because the constant \( 6.4 \) is based on calories.

### Step 3: Convert specific heat from Joules to calories
To convert Joules to calories, we use the conversion factor:
\[ 1 \, \text{cal} = 4.18 \, \text{J} \]
Thus, to convert \( 0.836 \, \text{J/g} \) to calories:
\[ \text{Specific Heat in cal/g} = \frac{0.836 \, \text{J/g}}{4.18 \, \text{J/cal}} \]

### Step 4: Calculate the specific heat in calories
Calculating the above gives:
\[ \text{Specific Heat in cal/g} = \frac{0.836}{4.18} \approx 0.2 \, \text{cal/g} \]

### Step 5: Substitute into the formula to find atomic weight
Now we substitute the specific heat back into the formula to find the atomic weight:
\[ \text{Atomic Weight} = \frac{6.4}{\text{Specific Heat in cal/g}} \]
\[ \text{Atomic Weight} = \frac{6.4}{0.2} \]

### Step 6: Perform the calculation
Calculating this gives:
\[ \text{Atomic Weight} = 32 \]

### Conclusion
The approximate atomic weight of the metal is **32**.

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