Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Select the correct answer.

What is the nuclear binding energy in joules for an atom of lithium? Assume the following:
Mass defect [tex]6.9986235 \times 10^{-29} \text{ kilograms}[/tex].
Use [tex]E = m c^2[/tex], with [tex]c = 3 \times 10^8 \text{ m/s}[/tex].

A. [tex]6.3 \times 10^{-12}[/tex] joules
B. [tex]0.6352 \times 10^{-8}[/tex] joules
C. [tex]6.3 \times 10^{-8}[/tex] joules
D. [tex]21.124 \times 10^{-21}[/tex] joules


Sagot :

Let's solve the problem step-by-step using the formula for nuclear binding energy [tex]\(E = mc^2\)[/tex].

### Step 1: Write Down the Given Values
- Mass defect ([tex]\(m\)[/tex]): [tex]\(6.9986235 \times 10^{-29}\)[/tex] kg
- Speed of light ([tex]\(c\)[/tex]): [tex]\(3 \times 10^8\)[/tex] m/s

### Step 2: Write Down the Formula
The formula to calculate the nuclear binding energy is:
[tex]\[ E = mc^2 \][/tex]

### Step 3: Substitute the Given Values into the Formula
[tex]\[ E = (6.9986235 \times 10^{-29} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 \][/tex]

### Step 4: Calculate the Energy
First, we need to square the speed of light:
[tex]\[ (3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \][/tex]

Next, multiply this result by the mass defect:
[tex]\[ E = 6.9986235 \times 10^{-29} \, \text{kg} \times 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \][/tex]

[tex]\[ E = 6.29876115 \times 10^{-12} \, \text{joules} \][/tex]

### Step 5: Match the Answer With the Choices
Comparing this result with the options provided:

A. [tex]\(6.3 \times 10^{-12}\)[/tex] joules

B. [tex]\(0.6352 \times 10^{-8}\)[/tex] joules

C. [tex]\(6.3 \times 10^{-8}\)[/tex] joules

D. [tex]\(21.124 \times 10^{-21}\)[/tex] joules

The correct answer is:
[tex]\[ 6.29876115 \times 10^{-12} \, \text{joules} \approx 6.3 \times 10^{-12} \, \text{joules} \][/tex]

Thus, the correct answer is:

A. [tex]\(6.3 \times 10^{-12}\)[/tex] joules.