Question

Calculate the Bohr's radius for the fifth orbit of the hydrogen atom.

Answer 1

1. Neil Bohr gave a model of the atom.
2. According to Neil Bohr, each shell of the atom has some amount of energy, therefore he gave another name for the shell is energy levels and an electron will revolve only in that orbit where its energy remains conserved.
3. Neil Bohr chose the hydrogen atom for his theory and he also gave the formula to calculate the radius of an orbit.
4. The formula to calculate the atomic radius is $\mathrm{r}=\frac{(0.0529){\mathrm{n}}^2}{\mathrm{Z}}$. Where n is the number of orbits and z is the atomic number of atoms.
5. Hydrogen has the atomic number 1.

Calculation.

Here, we have to calculate the radius for the fifth orbit of the hydrogen atom

$=\frac{0.0529\times {\left(5\right)}^2}{1}$

$$\begin{gathered} =0.0529\times 25 \\ =1.3225\mathrm{nm} \end{gathered}$$

The Bohr's radius for the fifth orbit of the hydrogen atom is $1.3225\mathrm{nm}$