If `a_(0)` is the Bohr radius, the radius of then `n=2` electronic orbit in triply ionized beryllium is

Options

A. `4a_(0)`
B. `a_(0)`
C. `a_(0)//4`
D. `a_(0)//16`

Explanation

To solve the problem of finding the radius of the n=2 electronic orbit in triply ionized beryllium, we will use the formula for the radius of an electron orbit in a hydrogen-like atom. The formula is given by:

\[ R_n = \frac{n^2 a_0}{Z} \]

where:
- \( R_n \) is the radius of the orbit,
- \( n \) is the principal quantum number (which is 2 in this case),
- \( a_0 \) is the Bohr radius,
- \( Z \) is the atomic number.

### Step-by-step Solution:

1. **Identify the Atomic Number (Z)**:
- Triply ionized beryllium has an atomic number \( Z = 4 \) (since beryllium has 4 protons in its nucleus).

2. **Identify the Principal Quantum Number (n)**:
- We are looking for the radius of the orbit when \( n = 2 \).

3. **Substitute the Values into the Formula**:
- Using the formula \( R_n = \frac{n^2 a_0}{Z} \):
\[ R_2 = \frac{2^2 \cdot a_0}{4} \]

4. **Calculate \( R_2 \)**:
- Calculate \( 2^2 \):
\[ 2^2 = 4 \]
- Substitute this back into the equation:
\[ R_2 = \frac{4 \cdot a_0}{4} \]
- Simplifying this gives:
\[ R_2 = a_0 \]

5. **Conclusion**:
- The radius of the n=2 electronic orbit in triply ionized beryllium is \( a_0 \).

### Final Answer:
The radius of the n=2 electronic orbit in triply ionized beryllium is \( a_0 \).

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