Considering Bohr's atomic model for hydrogen atom:
ion in its first excited state. , , ,
ion in its second excited state. only ,
ion for its ground state. only
ion in its first excited state is same as that for 
ion in its ground state. Choose the correct answer from the options given below: only only
Text Solution
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In Bohr's atomic model, the energy of an electron in an atom is given by the formula:
where 
is the atomic number and 
is the principal quantum number of the electron's orbit. Let's consider the implications:
For hydrogen (H), 
.
For helium ion 
.
For lithium ion ( 
), 
.
Now, identifying the relevant states:
Ground State: This corresponds to 
.
First Excited State: This corresponds to 
.
Second Excited State: This corresponds to 
.
Let's evaluate the energy comparisons:
Hydrogen Atom in Ground State: 
.
Helium Ion 
in the First Excited State: 
This matches the energy of hydrogen in its ground state.
Lithium Ion ( 
) in the Second Excited State:
This also matches the energy of hydrogen in its ground state.
From this analysis, we can conclude:
The energy of a hydrogen atom in its ground state is equal to the energy of a 
ion in its first excited state.
The energy of a hydrogen atom in its ground state also equals the energy of a 
ion in its second excited state.
Hence, statements and are correct.
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