Fisika kelas 12 | Fisika Inti dan Radioaktivitas

Introduction

This tutorial focuses on nuclear physics and radioactivity, specifically aimed at high school students studying these concepts in class 12. We will solve two problems: calculating the binding energy of a lithium nucleus and determining the remaining radioactive material after a specific time period. These calculations are fundamental in understanding nuclear stability and radioactive decay.

Step 1: Calculate the Binding Energy of Lithium-7

To find the binding energy of the lithium nucleus (3 Li 7), follow these steps:

1. Understand the Masses:

   • The mass of the lithium nucleus is given as 7.01822 atomic mass units (u).
   • The binding energy is calculated using the mass defect, which is the difference between the mass of the individual protons and neutrons and the mass of the nucleus.

2. Determine the Composition of Lithium-7:

   • Lithium-7 has 3 protons and 4 neutrons.
   • Mass of a proton ≈ 1.00728 u
   • Mass of a neutron ≈ 1.00866 u

3. Calculate the Total Mass of Free Nucleons:

   • Total mass of 3 protons = 3 × 1.00728 u = 3.02184 u
   • Total mass of 4 neutrons = 4 × 1.00866 u = 4.03464 u
   • Total mass = 3.02184 u + 4.03464 u = 7.05648 u

4. Calculate the Mass Defect:

   • Mass defect = Total mass of free nucleons - Mass of the nucleus
   • Mass defect = 7.05648 u - 7.01822 u = 0.03826 u

5. Convert Mass Defect to Binding Energy:

   • Use Einstein’s equation: E = mc²
   • Binding energy (in MeV) = Mass defect (u) × 931.5 MeV/u
   • Binding energy = 0.03826 u × 931.5 MeV/u ≈ 35.66 MeV

Step 2: Determine Remaining Radioactive Material

To calculate the remaining amount of a radioactive sample after a specific time, follow these steps:

1. Understand the Half-Life:

   • Half-life is the time required for half of the radioactive sample to decay. Here, the half-life is 5 days.

2. Calculate the Number of Half-Lives:

   • Given time = 20 days
   • Number of half-lives = Total time / Half-life = 20 days / 5 days = 4 half-lives

3. Calculate Remaining Sample:

   • Initial sample = 10 grams
   • After each half-life, the remaining quantity is halved:
     • After 1 half-life: 10 g / 2 = 5 g
     • After 2 half-lives: 5 g / 2 = 2.5 g
     • After 3 half-lives: 2.5 g / 2 = 1.25 g
     • After 4 half-lives: 1.25 g / 2 = 0.625 g

4. Final Calculation:

   • The remaining radioactive material after 20 days is approximately 0.625 grams.

Conclusion

In this tutorial, we covered how to calculate the binding energy of the lithium nucleus and determine the remaining amount of a radioactive sample over a period of time. Mastering these calculations not only strengthens your understanding of nuclear physics but also prepares you for more complex topics in this field. For further practice, consider exploring additional examples of binding energy and radioactive decay problems.