Question

A nucleus at rest splits into two nuclear parts having radii in the ratio of 1:3. Find the ratio of their velocities.

(a) 1:9

(b) 3:1

(c) 1:27

(d) 27:1

I had been asked this question by my school teacher while I was bunking the class.

Asked question is from Size of the Nucleus topic in division Nucleus of Physics – Class 12

Answer 1

The correct answer is (d) 27:1

To elaborate: Given: R1 = R0 (A1)^1/3 and R2 = R0 (A2)^1/3

\(\frac {R1}{R2} = (\frac {A1}{A2} ) ^{\frac {1}{3}} \) or \( \frac {A1}{A2} = (\frac {R1}{R2} )^3 = (\frac {1}{3} )^3 \)

\( \frac {A1}{A2} = \frac { 1}{27}\)

So, the ratio of their masses is given as:

\( \frac {m1}{m2} = \frac { 1}{27}\)

According to the principle of conservation of momentum, the magnitude of p1 = magnitude of p2

m1v1 = m2v2

\( \frac {v1}{v2} = \frac {m2}{m1} = \frac {27}{1}\) = 27:1.