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If the de Broglie wavelength of the electron in n th Bohr orbit in a hydrogen like atom is equal to 1.5 $π$ a₀ (a₀ is Bohr radius) then value of n / Z is :

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0.75

1.50

0.40

1.0

answer is D.

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Detailed Solution

$2 πr = nλ Also r_{H - like} = \frac{a_{0} \times n^{2}}{Z} Using 2 πr = nλ ∴ 2 π \times \frac{a_{0} \times n^{2}}{Z} = n \times \frac{3}{2} {πa}_{0} or \frac{n}{Z} = \frac{3}{4} = 0 .75$

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