Question

If radius of first bohr orbit of h atom is x

Answer 1

Helloo!!

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You mean to say that
If radius of first bohr orbit of Hydrogen atom is x then find it's de broglie's wavelength in 3rd orbit ??


--SOLUTION--

radius = n^2h^2/ 4π2mZe^2 

Therefore, r1/r3 = 1^2/3^2
r3 = 9/r1

= 9/x

Now, according to De Broglie; angular momentum of electron in 3rd orbit is:

mvr3 = 3h/2π   or  h/mv = 2πr3/3

λ = h/mv   where, λ is the de Broglie wavelength.
So,
λ = 2πr3/3

  = 2π x 9/3x

  = 6πx

hope it helps