The de Broglie wavelength of the electron in the n=4 orbit of Li^2+ is compared with that in the n=1 orbit of H. The ratio is

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The de Broglie wavelength of the electron in the $n = 4$ orbit of $Li X^{2 +}$ is compared with that in the $n = 1$ orbit of $H$ . The ratio is

Bohr's condition gives

nλ = 2 π r_{n}

, so

λ = 2 π r_{n} / n = 2 π a_{0} n / Z

. For

Li X^{2 +}

n = 4

2 π a_{0} (4/3)

. For H,

n = 1

2 π a_{0}

. The ratio is

4/3