If the average life time of an excited state of hydrogen is of the order of `10^(-8) s`, estimate how many rotations an electron makes when it is in the state `n = 2` and before it suffers a transition to state` n = 1 (Bohr radius a_(0) = 5.3 xx 10^(-11)m)`?

Explanation

To solve the problem, we need to estimate how many rotations an electron makes in the excited state \( n = 2 \) of a hydrogen atom before it transitions to the ground state \( n = 1 \). Given the average lifetime of the excited state is \( 10^{-8} \) seconds and the Bohr radius \( a_0 = 5.3 \times 10^{-11} \) m, we can follow these steps:

### Step 1: Calculate the velocity of the electron in the \( n = 2 \) orbit.
The velocity \( v_n \) of an electron in the \( n \)-th orbit of a hydrogen atom is given by the formula:

\[ v_n = \frac{Z e^2}{2 \epsilon_0 h n} \]
...