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In H-atom,if x is the radius of first Bohr orbit, de Broglie wavelength of an electron in the 3rd orbit is??

In H-atom,if x is the radius of first Bohr orbit, de Broglie wavelength of an electron in the 3rd orbit is??

Grade:12th Pass

1 Answers

Shobhit
3 Points
6 years ago
For a hydrogen atom, radius of nth orbit, rn = n2h2/ 4π2mZe2 Therefore, r1/r3 = 12/32 r3 = 9/r1 = 9/xNow, according to De Broglie; angular momentum of electron in 3rd orbit is:mvr3 = 3h/2π or h/mv = 2πr3/3Andλ = h/mv where, λ is the de Broglie wavelength.Therefore,λ = 2πr3/3 = 2π x 9/3x = 6πx

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