Question

In a hydrogen atom the de-broglie wavelength of an electron is $1.67nm$. The value of principal quantum number of the electron is: (give the closest interger value)

Answer 1

Given, de Broglie wavelength ($\lambda =1.67nm$)
$\therefore \lambda =2\pi r_n=2\pi a_{o}n\Rightarrow 16.7=2\times 3.14\times 0.529\times n\therefore n=\frac{16.7}{2\times 3.14\times 0.529}\approx 5$