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Mass defect and binding energy IB DP Physics Study Notes

Mass defect and binding energy IB DP Physics Study Notes - 2025 Syllabus

Mass defect and binding energy IB DP Physics Study Notes

Mass defect and binding energy IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • isotopes

  •  nuclear binding energy and mass defect

  •  the variation of the binding energy per nucleon with nucleon number

  • the mass-energy equivalence as given by E = mc2 in nuclear reactions

  •  the existence of the strong nuclear force, a short-range, attractive force between nucleons

Standard level and higher level: 7 hours
Additional higher level: 5 hours

IB DP Physics 2025 -Study Notes -All Topics

Mass defect and nuclear binding energy

  • To understand nuclear reactions, we have to use Einstein’s mass-energy equivalence relationship
  •  
  • This equation is probably the most famous of all
  • What E = mc2 means is that mass and energy are interchangeable.

EXAMPLE:

If one kilogram of anything is converted completely into energy, how much energy would be released?

SOLUTION:
\[
E = mc^2 = (1)(3.00 \times 10^8)^2 = 9.00 \times 10^{16} \, \text{J}.
\]

  • \(1 \, \text{megaton of TNT} = 4.184 \times 10^{15} \, \text{J}.\)
  • Finding the mass defect of a nuclear reaction takes three steps:

1. Find the mass of the reactants.
2. Find the mass of the products.
3. Find the difference in mass.

  • The difference in mass between the reactants and the products is called the mass defect (\(\Delta m\)).
  • The binding energy Eb of a nucleus is the amount of work or energy that must be expended to pull it apart.

A picture of the reaction 2(1H) + 2n → 4He might help:

 

∙The reverse process yields the same energy:

The ionizing effect of radiation

  • High exposure: Damage to the central nervous system and death within weeks.
  • Medium exposure: Damage to the stomach and intestines, leading to general sickness and diarrhea.
  • Low exposure: Hair loss, bleeding, and diarrhea.

FYI

  • There is evidence that cancer and genetic mutations can occur after exposure to radiation.

There are uses for radiation…

 

  • X-rays of teeth and bones
  • radiotherapy for cancer treatment

FYI

In radiotherapy radiation is used because rapidly dividing cancer cells are more susceptible to the damaging effects of radiation than healthy cells.

EXAMPLE:

What is the binding energy \(E_b\) in \(^4He\) in the nuclear reaction \(2(^1H) + 2n \rightarrow ^4He?\)

▶️Answer/Explanation

SOLUTION:

 Since \(^4He\) is \(5.044 \times 10^{-29} \, \text{kg}\) lighter than \(2(^1H) + 2n,\) we need to provide enough energy to make the additional mass of the constituents.
\[
E_b = (5.044 \times 10^{-29})(3.00 \times 10^8)^2 = 4.54 \times 10^{-12} \, \text{J}.
\]
 Thus, to pull apart the \(^4He\) and separate it into its constituents, \(4.54 \times 10^{-12} \, \text{J}\) are needed, which is the binding energy.

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