In the Bohr model the electron wavelength in an orbit satisfies nlambda = 2pi r_n with r_n propto n^2/Z. The ratio of the electron's de Broglie wavelength in the n=3 orbit of Li^2+ (Z=3) to that in the n=2 orbit of H is

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In the Bohr model the electron wavelength in an orbit satisfies $nλ = 2 π r_{n}$ with $r_{n} \propto n^{2} / Z$ . The ratio of the electron's de Broglie wavelength in the $n = 3$ orbit of $Li X^{2 +}$ ( $Z = 3$ ) to that in the $n = 2$ orbit of $H$ is

λ = 2 π r_{n} / n \propto n / Z

. For

Li X^{2 +}

n / Z = 3/3 = 1

; for H,

n / Z = 2

. Ratio

= 1/2