Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 40: Problem 63

\(^{8} \mathrm{Li}\) is an isotope that has a lifetime of less than one second. Its mass is \(8.022485 \mathrm{u} .\) Calculate its binding energy in \(\mathrm{MeV}\).

Short Answer

Expert verified
Based on the step-by-step solution provided, provide a short answer to the question: To calculate the binding energy of Lithium-8, first determine the number of protons and neutrons, which are 3 and 5, respectively. Then, find the total mass of protons and neutrons using their respective masses in atomic mass units. Next, calculate the mass defect by subtracting the mass of the Lithium-8 nucleus from the sum of the masses of its individual protons and neutrons. Finally, convert the mass defect to energy using the mass-energy equivalence formula E=mc² and the conversion factor 1u = 931.4941 MeV/c². This will give you the binding energy of Lithium-8 in MeV.

Step by step solution

01

Determine the number of protons and neutrons

As we are given Lithium-8, it has 8 nucleons in total, with 3 protons (since Lithium has an atomic number of 3) and the rest being neutrons. So there are 5 neutrons in the nucleus.
02

Calculate the mass of individual protons and neutrons

Knowing the atomic mass unit, which is approximately \(1.660539 \times 10^{-27} \mathrm{kg}\) and using the mass of a proton (\(1.007276 \mathrm{u}\)) and the mass of a neutron (\(1.008665 \mathrm{u}\)), we can calculate the mass of 3 protons and 5 neutrons. Total mass of protons: \(3 \times 1.007276 \mathrm{u}\) Total mass of neutrons: \(5 \times 1.008665 \mathrm{u}\)
03

Calculate the mass defect

Now, we will find the mass defect by subtracting the mass of the Lithium-8 nucleus from the sum of the masses of its individual protons and neutrons. Mass defect = (Total mass of protons + Total mass of neutrons) - Mass of Lithium-8 Mass defect = \((3 \times 1.007276 \mathrm{u} + 5 \times 1.008665 \mathrm{u}) - 8.022485 \mathrm{u}\)
04

Convert mass defect to energy

Using the mass-energy equivalence formula, E=mc², where 'E' is energy, 'm' is the mass defect, and 'c' is the speed of light (\(2.99792458 \times 10^8 \mathrm{m/s}\)). We will also use the conversion factor \(1 \mathrm{u} = 931.4941 \mathrm{MeV/c^2}\) in our calculation. Energy = Mass defect × c² Energy = Mass defect × (\(931.4941 \mathrm{MeV/c^2}\))
05

Calculate the binding energy

Now, plug in the mass defect from step 3 into the energy equation from step 4 and solve for the binding energy. Binding energy = (Mass defect) × (931.4941 MeV/c²) Make sure to include units in the final answer.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The specific activity of a radioactive material is the number of disintegrations per second per gram of radioactive atoms. a) Given the half-life of \({ }^{14} \mathrm{C}\) of \(5730 \mathrm{yr}\), calculate the specific activity of \({ }^{14} \mathrm{C}\). Express your result in disintegrations per second per gram, becquerel per gram, and curie per gram. b) Calculate the initial activity of a \(5.00-\mathrm{g}\) piece of wood. c) How many \({ }^{14} \mathrm{C}\) disintegrations have occurred in a \(5.00-\mathrm{g}\) piece of wood that was cut from a tree January \(1,1700 ?\)

In neutron stars, which are roughly \(90 \%\) neutrons and supported almost entirely by nuclear forces, which of the following binding-energy terms becomes relatively dominant compared to ordinary nuclei? a) the Coulomb term b) the asymmetry term c) the pairing term d) all of the above e) none of the above

The most common isotope of uranium, \({ }_{92}^{238} \mathrm{U},\) produces radon \({ }_{86}^{222} \mathrm{Rn}\) through the following sequence of decays: $$\begin{array}{c}{ }^{238} \mathrm{U} \rightarrow{ }^{234} \mathrm{Th}+\alpha,{ }^{234} \mathrm{Th} \rightarrow{ }^{234} \mathrm{~Pa}+\beta^{-}+\bar{\nu}_{e}, \\\\{ }_{91}^{234} \mathrm{~Pa} \rightarrow{ }_{92}^{234} \mathrm{U}+\beta+\bar{\nu}_{e},{ }^{234} \mathrm{U} \rightarrow{ }^{230} \mathrm{Th}+\alpha ,\\\\{ }_{91}^{230} \mathrm{Th} \rightarrow{ }_{90}^{226} \mathrm{Ra}+\alpha,{ }_{88}^{226} \mathrm{Ra} \rightarrow{ }_{86}^{222} \mathrm{Rn}+\alpha,\end{array}$$. A sample of \({ }_{92}^{238} \mathrm{U}\) will build up equilibrium concentrations of its daughter nuclei down to \({ }_{88}^{226} \mathrm{Ra} ;\) the concentrations of each are such that each daughter is produced as fast as it decays. The \({ }_{88}^{226} \mathrm{Ra}\) decays to \({ }_{86}^{222} \mathrm{Rn},\) which escapes as a gas. (The \(\alpha\) particles also escape, as helium; this is a source of much of the helium found on Earth.) In high concentrations, the radon is a health hazard in buildings built on soil or foundations containing uranium ores, as it can be inhaled. a) Look up the necessary data, and calculate the rate at which \(1.00 \mathrm{~kg}\) of an equilibrium mixture of \({ }_{92}^{238} \mathrm{U}\) and its first five daughters produces \({ }_{86}^{222} \mathrm{Rn}\) (mass per unit time). b) What activity (in curies per unit time) of radon does this represent?

Cobalt has a stable isotope, \({ }^{59} \mathrm{Co},\) and 22 radioactive isotopes. The most stable radioactive isotope is \({ }^{60} \mathrm{Co} .\) What is the dominant decay mode of this \({ }^{60}\) Co isotope? a) \(\beta^{+}\) b) \(\beta^{-}\) c) \(\mathrm{P}\) d) \(n\)

The half-life of a sample of \(10^{11}\) atoms that decay by alpha emission is \(10 \mathrm{~min} .\) How many alpha particles are emitted between the time interval 100 min and 200 min?
See all solutions

Recommended explanations on Physics Textbooks

Electricity

Read Explanation

Dynamics

Read Explanation

Force

Read Explanation

Modern Physics

Read Explanation

Classical Mechanics

Read Explanation

Radiation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free