JEE Main2014PhysicsNuclear PhysicsActual
A piece of bone of an animal from a ruin is found to have ¹⁴ C activity of 12 disintegrations per minute per gm of its carbon content. The ¹⁴ C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half life of ¹⁴ C is t _ 1 / 2 =5760 years)
Options
- A1672 years
- B2391 years
- C3291 years
- D4453 years
Correct answer
B. 2391 years
Step-by-step solution
Given, for ¹⁴ C aligned &A₀=16 dis ⁻¹ ~g ⁻¹ & ~A =12 dis ⁻¹ ~g ⁻¹ & t _ 1 / 2 =5760 years aligned Now, = 0.693 t _ 1 / 2 = 0.693 5760 per year Then, from, t = 2.303 ₁₀ A ₀ ~A = 2.303 5760 0.693 ₁₀ 16 12 = 2.303 5760 0.693 ₁₀ 1.333 = 2.303 5760 0.1249 0.693 =2390.81 2391 years