Question 372: Dual Nature of Matter and Radiation

Question

An electron in an excited state of Li
2+
ion has angular momentum $${{3h} \over {2\pi }}$$. The de Broglie wavelength of the electron in this state is p$$\pi$$a
0
(where a
0
is the Bohr radius). The value of p is

Accepted Answer

Angular momentum $$mvr = {{nh} \over {2\pi }}$$ where $$r = 3{a_0}$$ where $$n = 3$$, that is, electron in $$L{i^{2 + }}$$ is in second excited state
$$\lambda  = {h \over {mv}} = p\pi {a_0}$$
$$ \Rightarrow n = p\pi (mv{a_0}) = p\pi \left( {{{mvr} \over 3}} \right) = {{p\pi } \over 3}\left( {{{3h} \over {2\pi }}} \right) = {{ph} \over 2}$$
Therefore, $$p = 2$$.

Dual Nature of Matter and Radiation

An electron in an excited state of Li 2+ ion has angular momentum ${{3h} \over {2\pi }}. The de Broglie wavelength of the electron in this state is p\pi$a 0 (where a 0 is the Bohr radius). The value of p is

Integer / Numeric Answer Type