Ques. 1JEE Main 2024, 9 April (Morning Shift)
A star has 100\% helium composition. It starts to convert three 4He into one 12C via triple alpha process as 4He + 4He + 4He 12C + Q. The mass of the star is 2.0 1032 kg and it generates energy at the rate of 5.808 1030 W. The rate of converting these 4He to 12C is n 1042 s-1, where n is . [Take, mass of 4He = 4.0026 u, mass of 12C = 12 u]
Answer
15
Solution
Mass defect m = 3 4.0026 - 12 = 0.0078 u
so Q = 0.0078 931.5 7.266 MeV per reaction
= 7.266 1.6 10-13 J
Reactions per second: N = PQ = 5.808 10307.266 1.6 10-13 5 1042 s-1
Each reaction uses three 4He nuclei, so 4He is converted at 3N = 15 1042 s-1.
n = 15
Answer: 15
Note: The official NTA answer key gives 5. Our faculty team has re-checked this question and finds 15 correct, as explained above.