Question

The de - Broglie wavelength associated with the electron in the $n = 4$ level is :

• A. two times the de-Broglie wavelength of the electron in the ground state
• B. four times the de-Broglie wavelength of the electron in the ground state
• C. half of the de-Broglie wavelength of the electron in the ground state
• D. 1/4th of the de-Broglie wavelength of the electron in the ground state

Answer 1

Answer: (B)

four times the de-Broglie wavelength of the electron in the ground state

Answer 2

$\lambda=\frac{h}{m v}=\frac{h}{m\left(\beta \frac{z}{\mu}\right)}$,
where $\beta=$ constant and $n=$ orbit number
$\Rightarrow \lambda \propto n \Rightarrow \lambda_{4}=4 \lambda_{1}$