Recently many questions are constantly being unanswered so please answer this question meritnation teachers..if the radius of the first bohr orbit of hydrogen is taken as x then what is the de broglie wavelength in the 3rd orbit ??

For a hydrogen atom, radius of nth orbit, r_n = n²h²/ 4π2mZe² 

   Therefore, r₁/r₃ = 1²/3²

   r₃ = 9/r₁

  = 9/x

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

mvr₃ = 3h/2π   or  h/mv = 2πr₃/3

And

λ = h/mv   where, λ is the de Broglie wavelength.

Therefore,

λ = 2πr₃/3

  = 2π x 9/3x

  = 6πx