The element whose one atom has mass of `10.86xx10^(-26)` kg is (Atomic masses : B = 10.8 u, Ca = 40 u, Ag = 107.8 u, Zn = 65.4 u).

Options

A. boron
B. coalcium
C. silver
D. zinc

Explanation

To determine which element corresponds to the given atomic mass of \(10.86 \times 10^{-26}\) kg, we will follow these steps:

### Step 1: Convert the atomic mass from grams to kilograms
The atomic masses provided are in atomic mass units (u), which can also be expressed in grams per mole. We need to convert these values into kilograms for comparison with the given mass.

### Step 2: Use Avogadro's number
Avogadro's number is \(6.022 \times 10^{23}\), which represents the number of atoms in one mole of a substance. We will use this to find the mass of one atom of each element.

### Step 3: Calculate the mass of one atom for each element
We will calculate the mass of one atom for each element using the formula:
\[ \text{Mass of one atom} = \frac{\text{Molar mass (in grams)}}{\text{Avogadro's number}} \]

### Step 4: Compare the calculated masses with the given mass
We will compare the calculated mass of one atom for each element with the given mass of \(10.86 \times 10^{-26}\) kg.

### Step 5: Identify the correct element
The element whose atomic mass matches the calculated mass will be our answer.

Now, let's perform the calculations:

#### Calculation for Boron (B)
- Molar mass = 10.8 g/mol
- Mass of one atom:
\[ \text{Mass of one atom} = \frac{10.8 \, \text{g}}{6.022 \times 10^{23}} = \frac{10.8 \times 10^{-3} \, \text{kg}}{6.022 \times 10^{23}} \approx 1.79 \times 10^{-25} \, \text{kg} \]

#### Calculation for Calcium (Ca)
- Molar mass = 40 g/mol
- Mass of one atom:
\[ \text{Mass of one atom} = \frac{40 \, \text{g}}{6.022 \times 10^{23}} = \frac{40 \times 10^{-3} \, \text{kg}}{6.022 \times 10^{23}} \approx 6.64 \times 10^{-26} \, \text{kg} \]

#### Calculation for Silver (Ag)
- Molar mass = 107.8 g/mol
- Mass of one atom:
\[ \text{Mass of one atom} = \frac{107.8 \, \text{g}}{6.022 \times 10^{23}} = \frac{107.8 \times 10^{-3} \, \text{kg}}{6.022 \times 10^{23}} \approx 1.79 \times 10^{-25} \, \text{kg} \]

#### Calculation for Zinc (Zn)
- Molar mass = 65.4 g/mol
- Mass of one atom:
\[ \text{Mass of one atom} = \frac{65.4 \, \text{g}}{6.022 \times 10^{23}} = \frac{65.4 \times 10^{-3} \, \text{kg}}{6.022 \times 10^{23}} \approx 1.09 \times 10^{-25} \, \text{kg} \]

### Conclusion
After calculating the mass of one atom for each element, we find that the mass of one atom of Zinc (Zn) is approximately \(10.86 \times 10^{-26}\) kg, which matches the given mass.

Thus, the element whose one atom has a mass of \(10.86 \times 10^{-26}\) kg is **Zinc (Zn)**.