An electron in an excited state of Li2+ ion has angular momentum 3h/2π. The de Broglie wavelength of the electron in this state is pπa0 (where a0 is the Bohar radius). The value of p is

Engineering

Physics

Bohrs Model of Atom

de Broglie Hypothesis and Dual Nature

Question

An electron in an excited state of Li²⁺ ion has angular momentum 3h/2π. The de Broglie wavelength of the electron in this state is pπa₀ (where a₀ is the Bohar radius). The value of p is

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$L = \frac{nh}{2 π} = \frac{3 h}{2 π} \Rightarrow n = 3$

$mvr = \frac{nh}{2 π}$

$P = \frac{nh}{2 πr}$

$So, λ = \frac{h}{P} = \frac{2 πr}{n} = \frac{2 π}{3} (\frac{n^{2}}{2} a_{0})$

$∴ = \frac{2 π \times 3 a_{0}}{3} = 2 π a_{0} = P π a_{0}$

So P = 2