Question

The velocity of an electron in certain Bohr orbit of H-atom bears the ratio 1:275 to the velocity of light. (a) What is the quantum number 'n' of the orbit

Answer 1

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According to Bohr, the velocity of electron  of the n  

th

 stationary state for a hydrogen-like specie is expressed as :

v  

n

​  

=2.18×10  

6

×  

n

Z

​  

m/s

where Z=atomic number and n= orbit.

Given that v  

n

​  

:c=1:275

where c=velocity of light = 3×10  

8

 m/s

∴v  

n

​  

=c/275

or v  

n

​  

=  

275

3×10  

8

 

​  

=2.18×10  

6

×  

n

1

​  

 

n=2.18×10  

6

×  

3×10  

8

 

275

​  

 

n=1.998 or n=2

therefore the velocity of an electron in second (n=2) Bohr orbit of H-atom bears the ratio 1:275 to the velocity of light.

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