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 determine which statement is true for the isotopes \( _6^{14}C \), \( _7^{15}N \), and \( _8^{16}O \), we need to analyze the information provided about these isotopes.

### 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 (protons + neutrons)
- For \( _7^{15}N \):
- Atomic Number (Z) = 7 (number of protons)
- Mass Number (A) = 15 (protons + neutrons)
- For \( _8^{16}O \):
- Atomic Number (Z) = 8 (number of protons)
- Mass Number (A) = 16 (protons + neutrons)

2. **Calculate the Number of Neutrons**:
- The number of neutrons can be calculated using the formula:
\[ \text{Number of Neutrons} = \text{Mass Number} - \text{Atomic Number} \]
- For \( _6^{14}C \):
\[ \text{Neutrons} = 14 - 6 = 8 \]
- For \( _7^{15}N \):
\[ \text{Neutrons} = 15 - 7 = 8 \]
- For \( _8^{16}O \):
\[ \text{Neutrons} = 16 - 8 = 8 \]

3. **Summarize the Findings**:
- All three isotopes have the same number of neutrons, which is 8.
- The number of protons is different: 6 for Carbon, 7 for Nitrogen, and 8 for Oxygen.
- The mass numbers are different: 14 for Carbon, 15 for Nitrogen, and 16 for Oxygen.

4. **Conclusion**:
- The true statement regarding \( _6^{14}C \), \( _7^{15}N \), and \( _8^{16}O \) is that they all have the same number of neutrons (8).

### Final Answer:
The true statement is that **the number of neutrons is the same in all three isotopes**.