Which of the following statement is true for `._6^(14)C,_7^(15) N and ._8^(16)O`

Options

A. They have equal number of protons
B. The have equal number of electrons
C. They have equal number of neutrons
D. They have equal mass number

Answer

To solve the question regarding the statements true for \( _6^{14}C, _7^{15}N, \) and \( _8^{16}O \), we will analyze the atomic structure of each element and calculate their respective number of protons, neutrons, and electrons.

### Step-by-Step Solution:

1. **Identify the Atomic Number and Mass Number:**
- For \( _6^{14}C \):
- Atomic Number (Z) = 6 (number of protons)
- Mass Number (A) = 14
- For \( _7^{15}N \):
- Atomic Number (Z) = 7 (number of protons)
- Mass Number (A) = 15
- For \( _8^{16}O \):
- Atomic Number (Z) = 8 (number of protons)
- Mass Number (A) = 16

2. **Calculate the Number of Neutrons:**
- The number of neutrons (N) can be calculated using the formula:
\[ N = A - Z \]
- For Carbon \( (C) \):
\[ N_C = 14 - 6 = 8 \]
- For Nitrogen \( (N) \):
\[ N_N = 15 - 7 = 8 \]
- For Oxygen \( (O) \):
\[ N_O = 16 - 8 = 8 \]

3. **Determine the Number of Electrons:**
- Since all three atoms are neutral, the number of electrons is equal to the number of protons.
- For Carbon:
- Number of Electrons = 6
- For Nitrogen:
- Number of Electrons = 7
- For Oxygen:
- Number of Electrons = 8

4. **Conclusion:**
- From the calculations, we find that:
- Carbon has 8 neutrons.
- Nitrogen has 8 neutrons.
- Oxygen has 8 neutrons.
- Therefore, the true statement among the options provided is that \( _6^{14}C, _7^{15}N, \) and \( _8^{16}O \) all have equal numbers of neutrons.

### Final Answer:
The correct statement is that \( _6^{14}C, _7^{15}N, \) and \( _8^{16}O \) have equal numbers of neutrons.

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