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A nucleus of mass number 189 splits into two nuclei having mass numbers 125 and 64. The ratio of the radius of two daughter nuclei respectively is:

A

25:16:00

B

1:1

C

4:5

D

5:4

Step-by-Step Solution

  1. Identify the Formula: The radius (RR) of a nucleus is directly proportional to the cube root of its mass number (AA). The relationship is given by R=R0A1/3R = R_0 A^{1/3}, where R0R_0 is a constant (1.1×10−151.1 \times 10^{-15} m) .
  2. Identify Given Values:
  • Mass number of first daughter nucleus (A1A_1) = 125.
  • Mass number of second daughter nucleus (A2A_2) = 64.
  1. Calculate the Ratio:
  • Ratio R1R2=R0(A1)1/3R0(A2)1/3=(A1A2)1/3\frac{R_1}{R_2} = \frac{R_0 (A_1)^{1/3}}{R_0 (A_2)^{1/3}} = \left(\frac{A_1}{A_2}\right)^{1/3}.
  • R1R2=(12564)1/3\frac{R_1}{R_2} = \left(\frac{125}{64}\right)^{1/3}.
  1. Solve the Cube Roots:
  • 125=5\sqrt{125} = 5.
  • 64=4\sqrt{64} = 4.
  • Therefore, R1R2=54\frac{R_1}{R_2} = \frac{5}{4}.
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