Masses of two isobars `._(29)Cu^(64)` and `._(30)Zn^(64)` are `63.9298 u` and `63.9292 u`, respectively. It can be concluded from these data that .

Options

A. both the isobars are stable
B. `.^(64)Zn` is radioactive, decaying to `.^(64)Cu` through `beta-` decay
C. `.^(64)Cu` is radioactive, decaying to `.^(64) Zn` through `beta`-decay
D. `.^(64)Cu` is radioactive, decaying to `.^(64)Zn` through `gamma`-decay

Explanation

To solve the problem regarding the isobars Copper-64 and Zinc-64, we will analyze the information given about their masses and the nature of their decay.

### Step-by-Step Solution:

1. **Identify the Isobars**:
- We have two isobars: Copper-64 \((^{64}_{29}Cu)\) and Zinc-64 \((^{64}_{30}Zn)\). Isobars are nuclides that have the same mass number but different atomic numbers.

2. **Analyze the Masses**:
- The mass of Copper-64 is given as \(63.9298 \, u\) and the mass of Zinc-64 is \(63.9292 \, u\).
- Since the mass of Copper-64 is greater than that of Zinc-64, this indicates that Copper-64 is less stable and is likely to undergo decay.

3. **Determine the Type of Decay**:
- Since Copper-64 is decaying into Zinc-64, we can conclude that this is a beta decay process. In beta decay, a neutron in the nucleus is converted into a proton and an electron (beta particle) is emitted.
- The atomic number increases by 1 (from 29 for Copper to 30 for Zinc), which is characteristic of beta negative decay.

4. **Write the Decay Equation**:
- The decay can be represented as follows:
\[ ^{64}_{29}Cu \rightarrow ^{64}_{30}Zn + \beta^{-} + \bar{\nu} \]
- Here, \(\beta^{-}\) represents the emitted beta particle (electron), and \(\bar{\nu}\) represents the antineutrino.

5. **Conclude the Nature of the Isobars**:
- From the above analysis, we conclude that Copper-64 is radioactive and decays into Zinc-64 through beta decay.
- Since Zinc-64 is the product of this decay, it is stable and does not undergo further decay.

### Conclusion:
From the data provided, we can conclude that Copper-64 is radioactive and decays into Zinc-64 through beta decay.