Hydrogen-Deuterium Nuclear Fusion Energy Calculation And Implications

Hey guys! Today, we're diving into the fascinating world of nuclear physics, specifically focusing on nuclear fusion and the incredible amounts of energy it releases. We're going to break down a classic physics problem involving the fusion of hydrogen nuclei into deuterium, calculating just how much energy is unleashed in this process. So, buckle up and let's get started!

Understanding Nuclear Fusion and Energy Release

At its core, nuclear fusion is the process where two or more atomic nuclei combine to form a single, heavier nucleus. This is the powerhouse behind stars like our Sun, where immense temperatures and pressures force hydrogen atoms to fuse, creating helium and staggering amounts of energy. In our specific case, we're looking at a simpler, yet equally intriguing fusion reaction: two hydrogen nuclei (¹H) fusing to form a deuterium nucleus (²H). This reaction is a fundamental step in the proton-proton chain, the dominant fusion process in stars with masses similar to or smaller than the Sun.

The key to understanding the energy release lies in Einstein's famous equation, E=mc². This equation tells us that mass and energy are interchangeable. In nuclear fusion, the mass of the resulting nucleus (in our case, deuterium) is slightly less than the combined masses of the original nuclei (two hydrogen atoms). This seemingly tiny difference in mass, the mass defect, is converted into a tremendous amount of energy. The conversion factor is the speed of light squared (c²), a massive number that explains why even small mass differences translate to huge energy outputs.

The energy released in a nuclear reaction, often called the Q-value, can be calculated using the mass defect. We first determine the total mass of the reactants (the initial hydrogen nuclei) and the total mass of the products (the deuterium nucleus). The difference between these masses is the mass defect (Δm). We then plug this value into E=mc² to find the energy released. But there's a catch! The mass defect is typically expressed in atomic mass units (u), and the energy is often desired in electron-volts (eV) or megaelectron-volts (MeV). We'll need to use conversion factors to get our final answer in the correct units. One atomic mass unit (u) is equivalent to 931.5 MeV/c². This conversion factor makes the calculation much more straightforward. We simply multiply the mass defect (in u) by 931.5 MeV/c² to get the energy released in MeV. This method bypasses the need to explicitly calculate the energy in joules first, saving us a step and making the process more efficient. Now, let's apply these principles to our hydrogen-deuterium fusion problem!

Solving the Hydrogen-Deuterium Fusion Problem

Okay, let's break down the problem step by step. We have two hydrogen nuclei (¹H) fusing to form one deuterium nucleus (²H). We're given the masses of hydrogen (¹H) as 1.0078 u and deuterium (²H) as 2.0141 u. Our mission is to calculate the energy released in this fusion process, expressing our answer in megaelectron-volts (MeV).

First, we need to calculate the total mass of the reactants. Since we have two hydrogen nuclei, we multiply the mass of one hydrogen nucleus by two: 2 * 1.0078 u = 2.0156 u. This is the combined mass of the two hydrogen nuclei before they fuse.

Next, we have the mass of the product, which is the deuterium nucleus (²H), given as 2.0141 u. Now, we can determine the mass defect (Δm). This is the difference between the total mass of the reactants and the mass of the product: Δm = 2.0156 u - 2.0141 u = 0.0015 u. This seemingly small mass difference is the key to unlocking the energy released in the fusion process.

Now comes the exciting part: converting this mass defect into energy! We use Einstein's famous equation, E=mc². However, as we discussed earlier, we can use a handy conversion factor to simplify the calculation. We know that 1 u is equivalent to 931.5 MeV/c². So, we multiply our mass defect (0.0015 u) by this conversion factor: E = 0.0015 u * 931.5 MeV/c² per u = 1.39725 MeV. This is the energy released in the fusion of two hydrogen nuclei into one deuterium nucleus.

Rounding our result to a reasonable number of significant figures, we get approximately 1.40 MeV. This is a significant amount of energy released from the fusion of just two tiny nuclei! It highlights the immense power locked within the atomic nucleus and the potential of nuclear fusion as a clean and abundant energy source. So, the answer to our problem is that approximately 1.40 MeV of energy is released when two hydrogen nuclei fuse to form a deuterium nucleus.

Answering the Question and Real-World Implications

So, after our calculations, we've determined that the energy converted in the fusion of two hydrogen nuclei into a deuterium nucleus is approximately 1.40 MeV. Looking at the options provided, the closest answer is (A) 1.42 MeV. It's important to note that slight variations in the given masses or rounding during calculations can lead to minor differences in the final answer. However, our calculated value is well within the expected range, confirming our understanding of the process.

This type of calculation isn't just an academic exercise; it has profound implications for our understanding of the universe and our potential energy future. The fusion reactions we've discussed are the same ones powering the Sun and other stars. By understanding these processes, we can learn more about stellar evolution, the formation of elements, and the very nature of the cosmos. On a more practical level, researchers are working tirelessly to harness nuclear fusion as a clean and sustainable energy source here on Earth. Fusion power plants promise the potential for virtually limitless energy with minimal greenhouse gas emissions. The challenges are significant, requiring extreme temperatures and pressures to confine the plasma where fusion occurs. However, the potential rewards are so great that scientists and engineers around the world are pushing the boundaries of technology to make fusion energy a reality.

Imagine a future where our energy needs are met by mimicking the processes that power the stars! That's the promise of nuclear fusion, and our understanding of these fundamental reactions, like the fusion of hydrogen into deuterium, is a crucial step towards that goal. So, next time you look up at the Sun, remember the incredible fusion reactions happening within, and the potential they hold for our future.

Repair Input Keyword: Determine a energia convertida (em elétron-volt) quando dois núcleos de Hidrogênio (¹H) se fundem para gerar um núcleo de Deutério (²H), dado que a massa do Hidrogênio é 1,0078 u e a massa do Deutério é 2,0141 u.

SEO Title: Energia da Fusão Nuclear Hidrogênio-Deutério Cálculo e Implicações