Calculate the velocity of electron in the first Bohr orbit of hydrogen atom. Given that Bohr radius = `0.529 Å`, Planck's constant, `h = 6.626 xx 10^(-34)J`s, mass of electron `= 9.11 xx 10^(-31) kg and 1J = 1kg m^(2) s^(-2)`. Also calculate the velocity of electron in third orbit of `He^(+)` ion

Explanation

To solve the problem, we need to calculate the velocity of the electron in the first Bohr orbit of the hydrogen atom and then calculate the velocity of the electron in the third orbit of the He⁺ ion.

### Step 1: Calculate the velocity of the electron in the first Bohr orbit of hydrogen atom

The formula for the velocity of an electron in the nth orbit of a hydrogen atom is given by:

\[
v_n = \frac{Z \cdot e^2}{2 \cdot \epsilon_0 \cdot h} \cdot \frac{1}{n}
...