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Chapter 29: Problem 10

What is the binding energy of an \(\alpha\) particle (a \(^{4} \mathrm{He}\) nucleus)? The mass of an \(\alpha\) particle is \(4.00151 \mathrm{u}\).

Short Answer

Expert verified
Question: Calculate the binding energy of an 伪 particle with a mass of 4.00151 atomic mass units. Answer: To calculate the binding energy of the 伪 particle, follow these steps: 1. Determine the mass of the individual nucleons in the 伪 particle (two protons and two neutrons). 2. Calculate the mass defect by finding the difference between the total mass of the individual nucleons and the mass of the 伪 particle. 3. Convert the mass defect into energy using Einstein's equation \(E = mc^2\). 4. Convert the energy to megaelectronvolts (MeV) using the appropriate conversion factors. By following these steps, you can find the binding energy of the 伪 particle in MeV.

Step by step solution

01

Determine the mass of the individual nucleons

First, we need to find the mass of the individual nucleons in the 伪 particle. In an 伪 particle, there are two protons and two neutrons. The mass of a proton is approximately 1.00728 u, and the mass of a neutron is approximately 1.00867 u. So, we can calculate the total mass of the nucleons as follows: Total mass of nucleons = (2 脳 mass of a proton) + (2 脳 mass of a neutron)
02

Calculate the mass defect

Next, we will calculate the mass defect, which is the difference between the total mass of the individual nucleons and the mass of the 伪 particle. Given that the mass of the 伪 particle is 4.00151 u, we can calculate the mass defect as follows: Mass defect = Total mass of nucleons - Mass of 伪 particle
03

Convert the mass defect into energy

Now we'll convert the mass defect we found in the previous step into energy using Einstein's equation \(E = mc^2\). Note that we must first convert the mass defect from atomic mass units (u) to kilograms (kg) using the following conversion factor: 1 u = 1.660539 x \(10^{-27}\) kg. Once converted, we can then calculate the energy in joules (J) as follows: Energy = Mass defect (in kg) 脳 \((3.0 \times 10^8 m/s)^2\)
04

Convert the energy to MeV

Finally, we need to convert the energy found in the previous step from joules (J) to megaelectronvolts (MeV), which is a more commonly used unit for binding energy. To do this, we will use the following conversion factor: 1 J = 6.242 x \(10^{12}\) MeV. So, the binding energy will be: Binding energy = Energy (in J) 脳 conversion factor Following these steps, you will be able to find the binding energy of the 伪 particle in MeV.

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