Find the minimum laboratory kinetic energy, in MeV, of an α-particle required for ¹⁶₇N + ⁴₂He → ¹₁H + ¹⁹₈O, with ¹⁶₇N initially at rest. Masses are 16.006 u, 4.003 u, 1.008 u and 19.003 u; take 1 u c² = 930 MeV.
Physics · Nuclear physics
JEE Advanced 2022

Question

Find the minimum laboratory kinetic energy, in MeV, of an α-particle required for ¹⁶₇N + ⁴₂He → ¹₁H + ¹⁹₈O, with ¹⁶₇N initially at rest. Masses are 16.006 u, 4.003 u, 1.008 u and 19.003 u; take 1 u c² = 930 MeV.

Physics · Nuclear physics

JEE Advanced 2022

G1 Physics · Accepted Answer

Calculate Q from atomic masses: Q=[16.006+4.003−1.008−19.003]×930≈−1.86 MeV. For an endothermic two-body reaction with target mass 16u and projectile 4u, threshold K≈−Q(1+4/16)=2.325 MeV, i.e. about 2.32 MeV.