What is the mass defect of `""_(50)^(120)Sn` (atomic mass =119.902 200 u)? The hydrogen atom has a mass of 1.00783 u, and the neutron has a mass of 1.008 67 u.

Options

A. `6.9175xx10^(-28)kg`
B. `1.8202xx10^(-27)kg`
C. `8.0024xx10^(-28)kg`
D. `1.0687xx10^(-27)kg`

Answer

To find the mass defect of the nucleus of Tin-120 (represented as \( _{50}^{120}Sn \)), we will follow these steps:

### Step 1: Identify the number of protons and neutrons
The atomic number (50) indicates the number of protons in Tin-120. The mass number (120) indicates the total number of protons and neutrons.

- Number of protons (Z) = 50
- Mass number (A) = 120
- Number of neutrons (N) = A - Z = 120 - 50 = 70

### Step 2: Calculate the mass of protons and neutrons
Using the given masses:
- Mass of one proton (\( M_p \)) = 1.00783 u
- Mass of one neutron (\( M_n \)) = 1.00867 u

Now, calculate the total mass of protons and neutrons:
- Total mass of protons = \( 50 \times M_p = 50 \times 1.00783 \, \text{u} \)
- Total mass of neutrons = \( 70 \times M_n = 70 \times 1.00867 \, \text{u} \)

Calculating these:
- Total mass of protons = \( 50 \times 1.00783 = 50.3915 \, \text{u} \)
- Total mass of neutrons = \( 70 \times 1.00867 = 70.607 \, \text{u} \)

### Step 3: Calculate the combined mass of protons and neutrons
Now, add the total mass of protons and neutrons:
\[ \text{Total mass} = \text{Total mass of protons} + \text{Total mass of neutrons} = 50.3915 \, \text{u} + 70.607 \, \text{u} = 120.9985 \, \text{u} \]

### Step 4: Calculate the mass defect
The mass defect (\( \Delta m \)) is the difference between the combined mass of protons and neutrons and the actual mass of the nucleus:
\[ \Delta m = \text{Total mass of protons and neutrons} - \text{Mass of nucleus} \]
Given the mass of the nucleus of \( _{50}^{120}Sn \) is 119.902200 u:
\[ \Delta m = 120.9985 \, \text{u} - 119.902200 \, \text{u} = 1.0963 \, \text{u} \]

### Step 5: Convert the mass defect to kilograms (optional)
To convert the mass defect from atomic mass units (u) to kilograms, we use the conversion factor:
\[ 1 \, \text{u} = 1.660539 \times 10^{-27} \, \text{kg} \]
Thus,
\[ \Delta m \, \text{(in kg)} = 1.0963 \, \text{u} \times 1.660539 \times 10^{-27} \, \text{kg/u} \approx 1.824 \times 10^{-27} \, \text{kg} \]

### Final Answer
The mass defect of \( _{50}^{120}Sn \) is approximately \( 1.0963 \, \text{u} \) or \( 1.824 \times 10^{-27} \, \text{kg} \).

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