Calculate the energy released in the fusion reaction: 23He+12H→24He+11H_$$2^3He$$+_$$1^2H$$\$$rightarrow_2^4He$$+_$$1^1H$$

Ch 43: Nuclear Physics

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 43: Nuclear Physics

Problem 40

Chapter 42, Problem 40

Calculate the energy released in the fusion reaction: $_{2}^{3} H e +_{1}^{2} H \to_{2}^{4} H e +_{1}^{1} H$

Verified step by step guidance

Step 1: Understand the fusion reaction. Fusion is a process where two lighter nuclei combine to form a heavier nucleus, releasing energy. Identify the specific nuclei involved in the reaction (e.g., hydrogen isotopes like deuterium and tritium).

Step 2: Write the nuclear reaction equation. For example, in the fusion of deuterium (²H) and tritium (³H), the reaction is:

H_{2} + H_{3} \to {He}_{4} + n

. This produces helium-4 and a neutron.

Step 3: Calculate the mass defect. Determine the mass of the reactants (deuterium and tritium) and the products (helium-4 and neutron). Use the equation:

∆m = m

_reactants-m_products, where

∆m

is the mass defect.

Step 4: Convert the mass defect to energy using Einstein's equation:

E = mc^2

. Here,

m

is the mass defect and

c

is the speed of light (

3.00 \times 10^8 m/s

Step 5: Interpret the result. The energy calculated represents the energy released during the fusion reaction. This energy is typically expressed in joules or electron volts (eV).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Fusion

Nuclear fusion is the process where two light atomic nuclei combine to form a heavier nucleus, releasing a significant amount of energy. This reaction powers stars, including our sun, and occurs under extreme temperature and pressure conditions. Understanding fusion is crucial for calculating the energy released in such reactions.

Binding Energy

Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons. It is also the energy released when a nucleus is formed from these particles. The difference in binding energy before and after a fusion reaction determines the energy released, making it a key concept in energy calculations.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², states that mass can be converted into energy and vice versa. In fusion reactions, a small amount of mass is lost and converted into energy, which is released during the process. This principle is fundamental for understanding how energy is calculated in nuclear reactions.

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(a) What is the total energy absorbed by the tissue?

(b) What is the equivalent dose in rem?

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It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans) using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of $12$ mSv, applied to the whole body. By contrast, a chest x ray typically administers $0.20$ mSv to only $5.0$ kg of tissue. How many chest x rays would deliver the same total amount of energy to the body of a $75$ -kg person as one whole-body scan?

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At an archeological site, a sample from timbers containing $500$ g of carbon provides $2690$ decays/min. What is the age of the sample?

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Calculate the energy released in the fusion reaction: 23He+12H→24He+11H_2^3He+_1^2H\(\rightarrow\)_2^4He+_1^1H

Verified video answer for a similar problem:

Key Concepts

Nuclear Fusion

Binding Energy

Mass-Energy Equivalence

Calculate the energy released in the fusion reaction: $_{2}^{3} H e +_{1}^{2} H \to_{2}^{4} H e +_{1}^{1} H$