Question: 41: A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64 . The ratio of radius of two daughter nuclei respectively is
(1) 5: 4
(2) 25: 16
(3) 1: 1
(4) 4: 5
Answer: Option (1)
Explanation:
The radius of a nucleus is related to its mass number by the relation R = R_0 A^{1/3},
where R_0 is a constant and A is the mass number.
Let the radii of the two daughter nuclei be R_1 and R_2,
corresponding to mass numbers A_1 = 125 and A_2 = 64 respectively.
The ratio of their radii is given by
\frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3}.
Substituting the given values,
\frac{R_1}{R_2} = \left(\frac{125}{64}\right)^{1/3}.
Since 125 = 5^3 and 64 = 4^3,
we get \frac{R_1}{R_2} = \frac{5}{4}.
Therefore, the ratio of the radii of the two daughter nuclei is 5 : 4.
Hence, the correct answer is Option (1).