Binding Energy & Nuclear Radius — JEE Advanced 2016

Full transcript

Here's a classic JEE Advanced question: the binding-energy difference between nitrogen-15 and oxygen-15 is purely electrostatic — can you find the nuclear radius? Think carefully before picking your answer from the four options. Here is the key insight you need: the entire difference in binding energy between these two mirror nuclei comes from the electrostatic repulsion energy stored inside the nucleus. That single idea unlocks this whole problem. Nitrogen-15 has Z equal to 7, and oxygen-15 has Z equal to 8. The atomic mass difference works out to 0.002956 atomic mass units — write that value down and highlight it, because we will need it in the very next step. Multiply 0.002956 by 931.5 MeV per atomic mass unit and you get an energy difference of approximately 2.753 MeV. Circle that number — it is the electrostatic energy gap we need to match with our formula. Now apply the electrostatic energy formula. For oxygen Z is 8 so Z times Z minus 1 equals 56, and for nitrogen Z is 7 so Z times Z minus 1 equals 42. The difference is 14, giving us 12.096 divided by R. Set 12.096 divided by R equal to 2.753 MeV and solve: R equals 12.096 divided by 2.753, which gives approximately 3.42 femtometres. The correct answer is option C — and this elegant approach is exactly what JEE rewards every single time.