To determine which elements have negative electron affinity values, we'll analyze each option individually.

Understanding Electron Affinity

Electron Affinity (EA): The energy change when an electron is added to a neutral atom in the gas phase to form a negative ion.

Convention:

If energy is released (exothermic process), the electron affinity is considered positive.

If energy is absorbed (endothermic process), the electron affinity is considered negative.

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Option A: $\mathrm{Be} \rightarrow \mathrm{Be}^{-}$

Electronic Configuration of Be: $1s^2\,2s^2$

Analysis:

Adding an electron to beryllium means placing it into the higher energy $2p$ orbital.

Beryllium has a filled $2s$ subshell, so the added electron experiences higher energy and electron-electron repulsion.

Result: Energy is absorbed; the process is endothermic.

Conclusion: Electron affinity of Be is negative.

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Option B: $\mathrm{N} \rightarrow \mathrm{N}^{-}$

Electronic Configuration of N: $1s^2\,2s^2\,2p^3$

Analysis:

Nitrogen has a half-filled $2p$ subshell.

Adding an electron introduces repulsion in the half-filled orbital.

Result: Energy is absorbed; the process is endothermic.

Conclusion: Electron affinity of N is negative.

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Option C: $\mathrm{O} \rightarrow \mathrm{O}^{2-}$

Electronic Configuration of O: $1s^2\,2s^2\,2p^4$

Analysis:

First Electron Affinity (O to O⁻): Exothermic (energy released).

Second Electron Affinity (O⁻ to O²⁻): Endothermic because adding an electron to a negative ion requires energy due to electron-electron repulsion.

Overall Process (O to O²⁻): The second step dominates, making the overall process endothermic.

Conclusion: Electron affinity for forming $\mathrm{O}^{2-}$ is negative.

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Option D: $\mathrm{Na} \rightarrow \mathrm{Na}^{-}$

Electronic Configuration of Na: $1s^2\,2s^2\,2p^6\,3s^1$

Analysis:

Adding an electron fills the $3s$ orbital.

Sodium tends to lose an electron to form $\mathrm{Na}^+$, not gain one.

However, adding an electron is still an exothermic process due to the low energy of the $3s$ orbital.

Result: Energy is released; the process is exothermic.

Conclusion: Electron affinity of Na is positive.

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Option E: $\mathrm{Al} \rightarrow \mathrm{Al}^{-}$

Electronic Configuration of Al: $1s^2\,2s^2\,2p^6\,3s^2\,3p^1$

Analysis:

Adding an electron to the $3p$ orbital.

The process releases energy due to the addition of an electron to a partially filled orbital.

Result: Energy is released; the process is exothermic.

Conclusion: Electron affinity of Al is positive.

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Final Conclusion

Negative Electron Affinity Values (Endothermic Processes):

Option A: Beryllium ($\mathrm{Be}$)

Option B: Nitrogen ($\mathrm{N}$)

Option C: Oxygen forming $\mathrm{O}^{2-}$

Therefore, the correct answer is:

Option D: A, B, and C only

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Answer: Option D