The radius of the second Bohr orbit for hydrogen atom is : (Plank'c const. `h = 6.6262 xx 10^(-34) Js` , mass electron ` = 9.1091 xx 10^(-31)` Kg , charge of electron ` e = 1.60210 xx 10^(-19)` , permittivity of vaccum ` in_(0) = 8.854185 xx 10^(-12) kg^(-1) m^(-3) A^(2))`

Options

A. `1.65Å`
B. `4.76Å`
C. `0.529Å`
D. `2.12Å`

Explanation

To find the radius of the second Bohr orbit for a hydrogen atom, we can use the formula derived from Bohr's model of the atom. The formula for the radius of the nth orbit (R_n) is given by:

\[ R_n = \frac{n^2 h^2}{4 \pi^2 e^2 m} \]

where:
- \( R_n \) = radius of the nth orbit
- \( n \) = principal quantum number (for the second orbit, \( n = 2 \))
- \( h \) = Planck's constant
- \( e \) = charge of the electron
- \( m \) = mass of the electron
- \( \pi \) = constant (approximately 3.14)

However, we can simplify this formula for hydrogen (where \( Z = 1 \)) to:

\[ R_n = 0.529 \times n^2 \text{ Å} \]

### Step-by-step Solution:

1. **Identify the values**:
- For the second orbit, \( n = 2 \).
- The formula simplifies to \( R_n = 0.529 \times n^2 \).

2. **Substitute the value of n**:
- Substitute \( n = 2 \) into the formula:
\[ R_2 = 0.529 \times (2^2) \]

3. **Calculate \( n^2 \)**:
- Calculate \( 2^2 = 4 \).

4. **Calculate the radius**:
- Now substitute \( n^2 \) back into the equation:
\[ R_2 = 0.529 \times 4 \]
- Performing the multiplication:
\[ R_2 = 2.116 \text{ Å} \]

5. **Final Result**:
- The radius of the second Bohr orbit for the hydrogen atom is \( 2.116 \text{ Å} \).