The second orbit in `He^+` ion has radius as the first orbit in hydrogen atom.

Answer

To determine whether the statement "The second orbit in `He^+` ion has a radius equal to the first orbit in hydrogen atom" is true or false, we can follow these steps:

### Step 1: Understand the Radius of the Hydrogen Atom
The radius of the first orbit (n=1) in a hydrogen atom (H) is given as:
\[ R_1 = 0.53 \, \text{Å} \]

### Step 2: Use the Formula for the Radius of Orbits
The formula for the radius of the nth orbit in a hydrogen-like atom is:
\[ R_n = \frac{A_0 n^2}{Z} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( A_0 \) is the Bohr radius (0.53 Å for hydrogen),
- \( n \) is the principal quantum number (orbit number),
- \( Z \) is the atomic number.

### Step 3: Calculate the Radius of the Second Orbit in `He^+`
For the `He^+` ion, which has an atomic number \( Z = 2 \), we want to find the radius of the second orbit (n=2):
\[ R_2 = \frac{A_0 \cdot n^2}{Z} \]
Substituting the values:
\[ R_2 = \frac{0.53 \, \text{Å} \cdot 2^2}{2} \]
\[ R_2 = \frac{0.53 \, \text{Å} \cdot 4}{2} \]
\[ R_2 = \frac{2.12 \, \text{Å}}{2} \]
\[ R_2 = 1.06 \, \text{Å} \]

### Step 4: Compare the Radii
Now, we compare the radius of the second orbit in `He^+` (1.06 Å) with the radius of the first orbit in hydrogen (0.53 Å):
- The radius of the second orbit in `He^+` is 1.06 Å.
- The radius of the first orbit in hydrogen is 0.53 Å.

### Step 5: Conclusion
Since \( 1.06 \, \text{Å} \) (radius of the second orbit in `He^+`) is not equal to \( 0.53 \, \text{Å} \) (radius of the first orbit in hydrogen), the statement is **false**.

### Summary
The second orbit in `He^+` does not have a radius equal to the first orbit in hydrogen atom; instead, it is twice the radius of the hydrogen atom's first orbit.

---