 # de-brogile wavelenght of an electron in the nth orbit is Xn and the angular momentum is Jn then1. Jn directly proportational to Xn2. ang. mom. inverly prop. Xn3.Xn directly prop. to Jn2   4.Xn inversly prop. to Jn

13 years ago

In the Bohr’s model, the wavelength associated with the electron is given by the de Broglie wavelength equation:

λ = h/(mv)

and the standing wave condition that circumference = whole number of wavelengths. In the hydrogenic case, the number n is the principal quantum number.

2πr = nλn

These can be combined to get an expression for the angular momentum of the electron in orbit:

Jn = mvr = hr/λ

Applying the equation (Jn  = hr/λ) for wavelength of an electron in the nth orbit Xn and angular momentum Jn, we have:

hr

Jn = --------------

Xn

Hence Jn is inversely proportional to Xn; when r is fixed for nth orbit and h is plank constant.

12 years ago

10 years ago

Let us consider an electron revolving around a nucleus of an atom. The wave train formed by it is as shown in figure. Now, for the wave to be in phase, the circumference of the orbit around the nucleus should be an integral multiple of the wavelength of the wave.

λ=Xn

2Or=nλ,

where r is the radius of the orbit.

=nh/mν (from de Broglie’s equation)

Therefore,

Jn= (mvnλ)/2O

So,

Jn x Xn

Option A is Correct