A significant amount of energy is released during transmutations, which is evident from the kinetic energy of the released alpha or beta particle.  During a transmutation, a small amount of mass is changed directly into energy.  (Einstein developed the equation E=mc2 for this mass-energy equivalency.)  This can be shown by calculating the mass of a uranium-235 atom from its constituent parts.

From the calculations above, the atomic mass of uranium-235 is 236 u.  If you compare this value with the value in Table 7.5 on page 881 of the physics textbook, you will find a slight difference.  The table shows a value of 235.043 930 u.  Why is there a difference between the two values?  Where did the lost mass go?

The lost mass (called the mass defect), has been changed into binding energy holding the nucleons together.  This mass defect is used in nuclear reactions and helps explain the strong nuclear force needed to hold an atom together.

The law of conservation of energy was violated by this discovery as energy appears to be created.  Therefore, the law has been amended to the law of conservation of mass-energy, because Einsten showed that mass and energy are equivalent.  In fact, particle physicists often don't bother with masses but use mass equivalent as measured in MeV/c2.

Mass defect = mass products − mass reactants 

Calculating the amount of energy released in a nuclear reaction is possible by comparing the mass of the parent particle to the daughter particles.


Einstein's Mass - Energy Equivalence 

E = mc2

Quantity

Symbol

SI Unit

energy released in a nuclear reaction per decay

E

J
not eV

mass defect-the mass converted to energy in a nuclear reaction = mproducts - mreactants

m

kg

speed of light in a vacuum

c

m/s













Example Problem 5. What is the energy released when americium-241 transmutes?

From earlier we know the equation:

The masses were obtained from the National Institute of Standards and Technology or NIST.

NOTE: Because of the way the formula is written, the change in mass is negative.  The change is negative because mass is lost and, when mass is lost, energy is released.

The transmutation of one americium-241 atom releases 9.04 × 10-13 J.

Self-Check
 

Answer the following self-check question then click the "Check your work" bar to assess your response.

SC 5. a. What is the beta-positive decay reaction for sodium-22?

b. What is the energy released by the beta-positive decay of sodium-22?

 

 

SC 5.

a.

b. Given

 

Note: The sodium has 11 electrons but the neon has 10 electrons. One of the sodium's electrons drifts away during the decay but is not shown in the nuclear decay equation.


Required

The energy released by the beta-positive decay.


Analysis and Solution

Remember that there is an extra electron that must be taken into account in the final mass of the mass defect of a beta-positive, which is why the mass of the electron shows up twice: once for the beta-positive and once for the electron that drifts away.

Find the mass defect.

The negative mass shows that it is lost as it is changed into energy.

 

Method 1: Energy in Joules

Convert the mass defect into kilograms (kg).

Find the energy.

 

Method 2: Energy in Electron Volts

From "Mass-energy Equivalence" on page 793 of your physics textbook,

 

Warning: The value of 931.5 MeV/1u is not on the Physics Data Sheet for the Diploma Exam. To use this value you must derive it on the exam from values on the data sheet in order to receive full marks. Method 1 will be easier for the Diploma Exam.

 

Paraphrase

The energy released by the beta-positive decay is 2.92 × 10-13 J or 1.82 MeV.

 

Try This
Complete "Practice Problems" 1 to 3 on page 801 of your physics textbook. The masses can be found in "Table 7.5" on page 881 of the textbook.


Read
Read "Conservation Laws and Radioactive Decay" on page 798 of the textbook for an overview of the laws obeyed in nuclear reactions.


Try This
Complete both "Practice Problems" 1.(b) on page 803 of your physics textbook. You have already completed 1.(a) as TR 6.