If the radius of first orbit of hydrogen atom is R the de Broglie wavelength of an electron in the third orbit is ?

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Answer 1 · 2018-06-09T17:11:56

$6πR$ $"6πR"$

Radius of $n^{th}$ $"n"^"th"$ orbit is given by

$r_{n} = n^{2} R$ $"r"_"n" = "n"^2"R"$

Where $R$ $"R"$ is radius of first orbit of hydrogen atom.

So, Radius of $3^{rd}$ $3^"rd"$ orbit in terms of $R$ $"R"$ is

$r = 3^{2} R = 9R$ $"r" = 3^2"R = 9R"$

From de-Broglie hypothesis and Bohr’s postulate

$2πr = nλ$ $"2πr = nλ"$

Wavelength of electron in $3^{rd}$ $3^"rd"$ orbit from above equation is

$λ = "2πr"/"n"$

$color(white)(λ) = "2π × 9R"/3$

$color(white)(λ) = "6πR"$