Question

In: Physics

You are measuring the distance between the 6th and 2nd levels of the hydrogen atom while...

You are measuring the distance between the 6th and 2nd levels of the hydrogen atom while it is passing you at 99.99% of c.

A) What will this distance appear to be in the direction perpendicular to the traveling speed.

B) What will this distance appear to be in the direction parallel to the traveling speed.

Expert Solution

According to Bohr's atomic model, the atomic radius of n_th level is given by

(where a₀ = 0.0529 nm is Bohr radius)

So, for n =2 (i.e. second level) :

and for n=6 (i.e. sixth level):

So, the distance between sixth and second level is

According to special theory of relativity, the contraction in length in the direction of motion is given by

Where L is contracted length and L₀ is proper length.

Given the atom is moving with a velocity of 0.9999c.

(a) In the perpendicular direction of motion, there will not be any relativistic effect.

So, the distance between the levels will be

(b) In the parallel direction of motion, the length will get contracted. So, the observed length will be

We were unable to transcribe this image

L = Lo V1 - (v/c)2

We were unable to transcribe this image

genius_generous answered 6 months ago

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