Question:
Statement (A): As one considers orbits with higher values of \(n\) in hydrogen atom, the electric potential energy of the atom increases.
Statement (B): In Thomson's model, an atom is a spherical cloud of positive charges with electrons embedded in it.
Statement (C): The orbital picture in Bohr's model of the hydrogen atom was consistent with the uncertainty principle.
Statement (A): As one considers orbits with higher values of \(n\) in hydrogen atom, the electric potential energy of the atom increases.
Statement (B): In Thomson's model, an atom is a spherical cloud of positive charges with electrons embedded in it.
Statement (C): The orbital picture in Bohr's model of the hydrogen atom was consistent with the uncertainty principle.
Statement (B): In Thomson's model, an atom is a spherical cloud of positive charges with electrons embedded in it.
Statement (C): The orbital picture in Bohr's model of the hydrogen atom was consistent with the uncertainty principle.
Show Hint
Bohr’s model successfully explained hydrogen spectrum, but it failed to satisfy Heisenberg’s uncertainty principle and could not explain multi-electron atoms.
Updated On: Jun 26, 2026
- A, B and C are true
- A, B true, but C false
- B, C true, but A false
- A, C true, but B false
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The Correct Option is B
Solution and Explanation
Step 1: Analyze Statement (A).
For the hydrogen atom, \[ U=-\frac{ke^2}{r} \] where \(U\) is the electric potential energy.
As the principal quantum number \(n\) increases, the radius of orbit increases: \[ r_n\propto n^2 \] Hence, the magnitude of negative potential energy decreases and the value of potential energy becomes less negative.
For example: \[ -13.6\ \text{eV} \lt -3.4\ \text{eV} \] Thus, the electric potential energy increases with increasing \(n\).
Therefore, Statement (A) is true.
Step 2: Analyze Statement (B).
According to Thomson’s atomic model: \[ \text{Atom}=\text{positively charged sphere with electrons embedded in it} \] This is known as the “plum pudding model.”
Hence, Statement (B) is true.
Step 3: Analyze Statement (C).
Bohr’s model assumes electrons move in definite circular orbits with fixed radius and momentum simultaneously.
However, Heisenberg’s uncertainty principle states that position and momentum cannot both be known exactly at the same time: \[ \Delta x\,\Delta p \geq \frac{h}{4\pi} \] Thus, the definite orbital picture of Bohr’s model is not consistent with the uncertainty principle.
Therefore, Statement (C) is false.
Step 4: Final conclusion.
Hence, \[ \boxed{\text{A and B are true, but C is false}} \] Therefore, the correct option is \[ \boxed{(2)} \]
For the hydrogen atom, \[ U=-\frac{ke^2}{r} \] where \(U\) is the electric potential energy.
As the principal quantum number \(n\) increases, the radius of orbit increases: \[ r_n\propto n^2 \] Hence, the magnitude of negative potential energy decreases and the value of potential energy becomes less negative.
For example: \[ -13.6\ \text{eV} \lt -3.4\ \text{eV} \] Thus, the electric potential energy increases with increasing \(n\).
Therefore, Statement (A) is true.
Step 2: Analyze Statement (B).
According to Thomson’s atomic model: \[ \text{Atom}=\text{positively charged sphere with electrons embedded in it} \] This is known as the “plum pudding model.”
Hence, Statement (B) is true.
Step 3: Analyze Statement (C).
Bohr’s model assumes electrons move in definite circular orbits with fixed radius and momentum simultaneously.
However, Heisenberg’s uncertainty principle states that position and momentum cannot both be known exactly at the same time: \[ \Delta x\,\Delta p \geq \frac{h}{4\pi} \] Thus, the definite orbital picture of Bohr’s model is not consistent with the uncertainty principle.
Therefore, Statement (C) is false.
Step 4: Final conclusion.
Hence, \[ \boxed{\text{A and B are true, but C is false}} \] Therefore, the correct option is \[ \boxed{(2)} \]
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