How many times does the electron go round the firstBohr orbit of hydrogen atoms in 1 s?

To determine how many times an electron goes around the first Bohr orbit of a hydrogen atom in 1 second, we can follow these steps:

1. ### Break Down the Problem

We need to find the time taken for one complete revolution of the electron in the first Bohr orbit and then calculate how many such revolutions occur in 1 second.

2. ### Relevant Concepts

The radius of the first Bohr orbit $r_1$ for a hydrogen atom is given by: $r_1 = 5.29 \times 10^{-11} \, \text{m}$

The velocity $v$ of the electron in the first orbit can be determined using the formula: $v = \frac{e^2}{4 \pi \epsilon_0 \hbar} \text{ (where relevant constants can be plugged in to find v)}$ However, it's known that the orbital velocity for the first orbit is about: $v \approx 2.19 \times 10^6 \, \text{m/s}$

The circumference $C$ of the first orbit is: $C = 2 \pi r_1$

3. ### Analysis and Detail

1. Calculate the circumference $C$: $C = 2 \pi (5.29 \times 10^{-11}) \approx 3.33 \times 10^{-10} \, \text{m}$

2. Calculate the time for one complete revolution $T$: The time $T$ for one revolution is given by the formula: $T = \frac{C}{v} = \frac{3.33 \times 10^{-10}}{2.19 \times 10^6} \approx 1.52 \times 10^{-16} \, \text{s}$

3. Calculate the number of revolutions per second $n$: The number of revolutions per second $n$ is: $n = \frac{1 \, \text{s}}{T} = \frac{1}{1.52 \times 10^{-16}} \approx 6.58 \times 10^{15}$

4. ### Verify and Summarize

The calculations appear correct, and the results are consistent with known physics for the hydrogen atom.

Final Answer

The electron goes around the first Bohr orbit of a hydrogen atom approximately $6.58 \times 10^{15}$ times in 1 second.