Question

Calculate the average binding energy per nucleon of 2656​Fe. Express your answer using four significant figures. Part B Calculate the average binding energy per nucleon of 92238​U. Express your answer using four significant figures.

Answer 1

The average binding energy per nucleon of
`\(^(56)\text{Fe}\`) is approximately 8.79 MeV.

Step-by-step explanation:

The average binding energy per nucleon is calculated by dividing the total binding energy of the nucleus by the total number of nucleons present. For
`\(^(56)\text{Fe}\),` the total binding energy is obtained by multiplying its mass defect with the speed of light squared
`(\(E = \Delta mc^2\)).` Dividing this by the total number of nucleons (56 for iron-56) yields the average binding energy per nucleon. This calculation results in approximately 8.79 MeV. This high value indicates a relatively stable nucleus due to a strong binding force holding the nucleons together.

The calculation involves determining the mass defect, which signifies the difference between the mass of individual nucleons and the actual nucleus. This difference multiplied by
`\(c^2\)` provides the energy required to bind the nucleons together.

Dividing this total binding energy by the total number of nucleons gives the average binding energy per nucleon, which serves as a crucial parameter in understanding the stability of a nucleus. In the case of
`\(^(56)\text{Fe}\),` its significant average binding energy per nucleon showcases its stability, essential for various nuclear processes and its abundance in the universe.

This method, applied consistently to different elements or isotopes, helps evaluate their stability and energy characteristics, guiding various fields from nuclear physics to astrophysics.

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Answer 2

To calculate the average binding energy per nucleon, we divide the total binding energy by the total number of nucleons. For 2656Fe, the average binding energy per nucleon is 2352.29 MeV, and for 92238U, it is 19.4 MeV.

Step-by-step explanation:

To calculate the average binding energy per nucleon, we divide the total binding energy of the nucleus by the total number of nucleons in the nucleus. We can use the equation BE = (Am)c², where Am is the mass defect. In the case of 26Fe, we need to find the mass defect and then divide the binding energy by the total number of nucleons. We can use the information from Example 21.3, which states that the binding energy per nucleon for 56Fe is 493.9 MeV. Therefore, the average binding energy per nucleon for 2656Fe would be:

(2656/56) * 493.9 MeV = 2352.29 MeV/nucleon (rounded to four significant figures).

Similarly, for 92U238, we can use the information from Example 15.4.3, which states that the binding energy per nucleon for 235U is about 7.6 MeV. Therefore, the average binding energy per nucleon for 92238U would be:

(238/92) * 7.6 MeV = 19.4 MeV/nucleon (rounded to four significant figures).