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

Isha Keshav , 6 Years ago
Grade 11
anser 1 Answers
Arun

Last Activity: 6 Years ago

For a hydrogen atom, radius of nth orbit, rn = n2h2/ 4π2mZe

   Therefore, r1/r3 = 12/32

   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

And

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

Therefore,

λ = 2πr3/3

  = 2π 9/3x

  = 6πx

 

Regards

Arun

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