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If the mass defect of \({ }_{4} \mathrm{X}^{9}\) is \(0.090 \mathrm{amu}\), then the binding energy per nucleon is (1 amu = 921.5 MeV) (a) \(83.0 \mathrm{MeV}\) (b) \(9.315 \mathrm{MeV}\) (c) \(8.38 \mathrm{MeV}\) (d) \(931.5 \mathrm{MeV}\)

Short Answer

Expert verified
The binding energy per nucleon is approximately 9.315 MeV.

Step by step solution

01

Understand the Concept

The binding energy per nucleon indicates how much energy is required to remove a nucleon from the nucleus on average. It can be calculated by dividing the total binding energy by the number of nucleons.
02

Calculate Total Binding Energy

To find the total binding energy, multiply the mass defect by the energy equivalent of 1 amu. Given mass defect is 0.090 amu and 1 amu = 921.5 MeV, the total binding energy is calculated as: \[0.090 ext{ amu} \times 921.5 ext{ MeV/amu} = 82.935 ext{ MeV}.\]
03

Count the Number of Nucleons

The symbol \(_{4} X^{9}\) indicates that there are 9 nucleons (protons and neutrons) in the nucleus.
04

Calculate Binding Energy Per Nucleon

Divide the total binding energy by the number of nucleons to find the binding energy per nucleon:\[\frac{82.935 ext{ MeV}}{9} \approx 9.215 ext{ MeV}.\]
05

Match to Closest Option

The calculated binding energy per nucleon (9.215 MeV) is closest to the answer option (b) 9.315 MeV.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Defect
When discussing nuclear physics, the term "mass defect" is crucial. It refers to the apparent loss of mass that occurs when protons and neutrons combine to form a nucleus. Let's break this down. Each proton and neutron has a specific mass when isolated. However, when they bind together in a nucleus, the total mass is slightly less than the sum of their individual masses. This difference is the mass defect. Mass defect occurs due to the conversion of mass into binding energy, which holds the nucleus together. This concept is rooted in Einstein's famous equation, \[E=mc^2\]. In this context, it means that the missing mass has been converted into energy. Understanding mass defect is important because it directly relates to the stability and energy of the nucleus. It's the mass defect that helps us calculate the binding energy of the nucleus and understand how stable a particular isotope is. More mass defect means stronger binding energy, indicating a more stable nucleus. Mass defect is a central idea when examining nuclear reactions or decay.
Energy Equivalent of Amu
In nuclear physics, one atomic mass unit (amu) plays a vital role in calculations and is intricately related to energy. An atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom. It's a small unit of mass typically used to express atomic and molecular weights. However, in nuclear contexts, its energy equivalent becomes pivotal. The energy equivalent of 1 amu is approximately 921.5 MeV (mega electron volts). Why is this value so important? It allows scientists to translate mass differences—like those determined by mass defect—into measurable energy values.
Applying this concept:
  • Calculate energy released or absorbed in nuclear reactions.
  • Determine the binding energy of nuclei.
Without understanding the energy equivalent of an amu, it would be challenging to relate mass and energy changes within the nucleus. This conversion helps link theoretical calculations to observable energy changes in nuclear processes.
Nucleons in a Nucleus
The term "nucleons" refers to the particles present in an atomic nucleus, specifically protons and neutrons. These are the building blocks of a nucleus. Understanding the composition and number of nucleons in a nucleus is fundamental for nuclear chemistry and physics. In notation such as \(_{4} X^{9}\), the number of nucleons is given as the superscript (9, in this case), representing the total number of protons and neutrons. Subscripts denote the number of protons (atomic number), which for many elements also suggests the element's position in the periodic table.
Here's why counting nucleons is essential:
  • It helps in calculating the atomic mass of an atom.
  • It allows determination of nuclear stability, as the ratio of protons to neutrons affects stability.
  • It plays a role in identifying isotopes, which possess the same number of protons but different numbers of neutrons.
Recognizing the number of nucleons provides insight into an element's properties and reactions, making it a cornerstone concept in nuclear studies.

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Most popular questions from this chapter

When a radioactive element emits successively one \(\alpha\) particle and two \(\beta\) particles, the mass number of the daughter element (a) is reduced by 4 units (b) remains the same (c) is reduced by 2 units (d) is increased by 2 units

A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room? (a) 300 days (b) 10 days (c) 100 days (d) 1000 days

In the nuclear reaction: \({ }_{3} \mathrm{Li}^{7}+{ }_{1} \mathrm{H}^{1} \longrightarrow 2{ }_{2} \mathrm{He}^{4}\) the mass loss is nearly \(0.02 \mathrm{amu}\). Hence, the energy released (in units of million \(\mathrm{kcal} / \mathrm{mol}\) ) in the process is approximately (a) 100 (b) 200 (c) 400 (d) 600

In a radioactive decay, an emitted electron comes from (a) the nucleus of atom (b) the orbit with principal quantum number 1 (c) the inner orbital of the atom (d) the outermost orbit of the atom

Which of the following option is correct? (a) In living organisms, circulation of \({ }^{14} \mathrm{C}\) from atmosphere is high so the carbon content is constant in organism. (b) carbon dating can be used to find out the age of earth crust and rocks (c) radioactive absorption due to cosmic radiation is equal to the rate of radioactive decay, hence the carbon content remains constant in living organism (d) carbon dating can not be used to determine concentration of \({ }^{14} \mathrm{C}\) in dead beings.

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