Question

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason R : The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below :

• A. Both A and R are true but R is NOT the correct explanation of A.
• B. A is false but R is true.
• C. Both A and R are true and R is the correct explanation of A.
• D. A is true but R is false.

Hint:

The Bohr model is a foundational model in atomic physics but has limitations. Remember that it works well for single-electron systems because it neglects the complexities of electron-electron interactions. For multi-electron atoms, more sophisticated models like the quantum mechanical model are necessary.

Answer 1

The Correct Option is C

The question provides an assertion and a reason regarding the Bohr model.

• Assertion (A): The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
• Reason (R): The formulation of Bohr model does not include repulsive force between electrons.

Let's evaluate both statements:

1. Understanding the Assertion (A):
   • The Bohr model, introduced by Niels Bohr in 1913, describes the hydrogen atom or hydrogen-like ions (such as He⁺, Li²⁺, etc.) which contain only one electron. It accounts for the quantization of angular momentum and provides expressions for the energy levels of these one-electron systems. The model works effectively only for single-electron systems because it does not consider electron-electron interactions, which are significant in multi-electron atoms.
2. Understanding the Reason (R):
   • The Bohr model assumes that electrons orbit the nucleus in fixed paths without accounting for the repulsive forces between multiple electrons, as it focuses solely on the electrostatic force of attraction between a single electron and the positively charged nucleus. This is why it is not applicable to multi-electron atoms where inter-electronic repulsions play an important role.

Now, let's match these with the given options:

• Option 1: Both A and R are true but R is NOT the correct explanation of A.
• Option 2: A is false but R is true.
• Option 3: Both A and R are true and R is the correct explanation of A. (Correct Answer)
• Option 4: A is true but R is false.

Conclusion: Both the assertion and reason are true, and importantly, the reason correctly explains why the Bohr model is limited to hydrogen and hydrogen-like atoms. Therefore, the correct answer is: Both A and R are true and R is the correct explanation of A.

Answer 2

Assertion A states that the Bohr model is applicable to hydrogen and hydrogen-like atoms only. 
Hydrogen-like atoms are those that have only one electron, such as \( He^+, Li^{2+}, Be^{3+} \), etc. 
The Bohr model successfully explains the atomic spectra of hydrogen and these single-electron species. 
For atoms with more than one electron, the Bohr model fails to predict the correct spectra. 
Thus, Assertion A is true. Reason R states that the formulation of the Bohr model does not include the repulsive force between electrons. 
The Bohr model is a simplified model of the atom that considers electrons orbiting the nucleus in specific quantized energy levels. 
It does not take into account the inter-electronic repulsions that are significant in multi-electron atoms. 
The absence of consideration for electron-electron repulsion is a primary reason why the Bohr model is only accurate for single-electron systems. Thus, Reason R is also true. Furthermore, the reason R correctly explains why the Bohr model is limited to hydrogen and hydrogen-like atoms. The simplicity of having only one electron eliminates the complexities arising from electron-electron interactions, which are not accounted for in the Bohr model. Therefore, Reason R is the correct explanation of Assertion A.