JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Modern Physics

Considering Bohr's atomic model for hydrogen atom:
(A) the energy of H atom in ground state is same as energy of

He^{+}

ion in its first excited state.
(B) the energy of H atom in ground state is same as that for

Li^{++}

ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of

He^{+}

ion for its ground state.
(D) the energy of

He^{+}

ion in its first excited state is same as that for

Li^{++}

ion in its ground state

Choose the correct answer from the options given below:

Answer: (B)

Solution

In Bohr's model a level has energy proportional to

\frac{Z ^{2}}{n ^{2}}

. For hydrogen in its ground state (

Z = 1, n = 1

) this is

1

. For

He^{+}

in its first excited state (

Z = 2, n = 2

) it is

\frac{4}{4} = 1

, equal to hydrogen's ground state, so (A) holds. For

Li^{++}

in its second excited state (

Z = 3, n = 3

) it is

\frac{9}{9} = 1

, again equal, so (B) holds. The ground states of

He^{+}

(

\frac{4}{1} = 4

) and

Li^{++}

(

\frac{9}{1} = 9

) do not match hydrogen's ground state, and the

He^{+}

first excited state (

1

) does not match the

Li^{++}

ground state (

9

), so (C) and (D) fail. The correct statements are (A) and (B).

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Single correct option