Which Energy State Of The Triply Ionized Beryllium (Be+++) Has The Same Orbital Radius As That Of The Ground State Of Hydrogen? Compare The Energies Of The Two States. 

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Question

Which energy state of the triply ionized beryllium (Be+++) has the same orbital radius as that of the ground state of hydrogen? Compare the energies of the two states. 

Solution

Correct option is

4

The radius of the nth orbit of hydrogen-like atoms is given by 

           .  

  

where  is a constant. For the ground state (n = 1) of hydrogen atom (Z = 1), we have  

           r = k. 

Let n be the energy state of Be+++(Z = 4) for which the orbital radius is k(same as of hydrogen in ground state). Putting r = k and Z = 4 in eq. (i), we get 

          

.     

The energy of electron in the nth state of hydrogen-like atoms is given by       

           

.      

For   Be+++, Z = 4, and n = 2; for H, Z = 1 and n = 1.   

.

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