The isotope ⁶⁴Zn has a nuclear radius of 4.8 × 10−¹⁵ m.Which of the following is the mass number of an isotope for which the nuclear radius is 3.6 × 10−¹⁵ m? A)3 B)1 C)9 D)27 E)48

Question

Quizplus · Accepted Answer

The nuclear radius R of an isotope is related to its mass number A by the formula R = R0A^(1/3), where R0 is a constant. Given that the radius of one isotope is 4.8 × 10^−15 m for a mass number of 64, and we need to find the mass number for a radius of 3.6 × 10^−15 m, we can set up a ratio based on the formula: (4.8/3.6) = (A2/64)^(1/3). Solving for A2 gives us 27, indicating that the mass number of the isotope with the smaller radius is 27.

The Isotope 64Zn Has a Nuclear Radius of 4

The Isotope ⁶⁴Zn Has a Nuclear Radius of 4