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"#

Radius of #"n"^"th"# orbit is given by

#"r"_"n" = "n"^2"R"#

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

So, Radius of #3^"rd"# orbit in terms of #"R"# is

#"r" = 3^2"R = 9R"#

From de-Broglie hypothesis and Bohr’s postulate

#"2πr = nλ"#

Wavelength of electron in #3^"rd"# orbit from above equation is

#λ = "2πr"/"n"#

#color(white)(λ) = "2π × 9R"/3#

#color(white)(λ) = "6πR"#