# If the radius of first orbit of hydrogen atom is R the de Broglie wavelength of an electron in the third orbit is ?

##### 1 Answer
Jun 9, 2018

$\text{6πR}$

#### Explanation:

Radius of $\text{n"^"th}$ orbit is given by

$\text{r"_"n" = "n"^2"R}$

Where $\text{R}$ is radius of first orbit of hydrogen atom.

So, Radius of ${3}^{\text{rd}}$ orbit in terms of $\text{R}$ is

$\text{r" = 3^2"R = 9R}$

From de-Broglie hypothesis and Bohr’s postulate

$\text{2πr = nλ}$

Wavelength of electron in ${3}^{\text{rd}}$ orbit from above equation is

λ = "2πr"/"n"

color(white)(λ) = "2π × 9R"/3

color(white)(λ) = "6πR"