Wave nature of matter

Remember concepts with our Masterclasses.

80k Users

60 mins Expert Faculty Ask Questions

Question

An electron in an excited state of $L i^{2 +}$ ion has angular momentum $3 h / 2 π$ . The de Broglie wavelength of the electron in this state is $P π a_{0}$ (where $a_{0}$ is the Bohr radius). The value of P is

Moderate

Solution

$\begin{array}{l} B o h r' s P o s t u l a t e, \frac{nh}{2 π} = \frac{3 h}{2 π} \\ \Rightarrow n = 3 \\ Radius = r = \frac{a_{0} n^{2}}{z} \\ \Rightarrow r = a_{0} (\frac{9}{3}) = 3 a_{0} \\ W a v e l e n g t h = λ = \frac{h}{m v} = \frac{h r}{m v r} = \frac{h r}{\frac{nh}{2 π}} = \frac{2 π r}{n} \\ \Rightarrow λ = \frac{2 π 3 a_{0}}{3} \\ \Rightarrow λ = 2 π a_{0} \\ S o, P = 2 \end{array}$

Ready to Test Your Skills?

Check Your Performance Today with our Free Mock Tests used by Toppers!

Talk to our academic expert!

Create Your Own Test
Your Topic, Your Difficulty, Your Pace

Similar Questions

A Photoelectric material having work-function $ϕ_{0}$ is illuminated with light of wavelength $λ$ $(λ < \frac{h c}{ϕ_{0}})$ . The fastest photoelectron has a de Broglie wavelength $λ_{d}$ . A change in wavelength of the incident light by $△ λ$ results in a change $Δ λ_{d}$ in $λ_{d}$ . Then the ratio $Δ λ_{d} / Δ λ$ is proportional to $\frac{λ_{d}^{a}}{λ^{b}}$ . The value of $a + b$ is