Question

Given below are two statements :
Statement I : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principal quantum number.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Hint:

Always use the proportionality \(v \propto \frac{Z}{n}\) for velocity and \(E \propto -\frac{Z^2}{n^2}\) for energy to quickly evaluate such conceptual statements in Bohr's theory.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In the Bohr model of the atom, the velocity of an electron in a specific orbit depends on the atomic number (\(Z\)) and the principal quantum number (\(n\)).
Step 2: Key Formula or Approach:
The velocity of an electron in the \(n^{th}\) orbit is given by:
\[ v_n = v_0 \times \frac{Z}{n} \]
where \(v_0\) is a constant (\(\approx 2.18 \times 10^6 \text{ m/s}\)).
Step 3: Detailed Explanation:
1. Analysis of Statement I: From the formula \(v \propto Z\), velocity is directly proportional to the positive charge on the nucleus (atomic number \(Z\)). Therefore, if the positive charge decreases, the magnitude of velocity should decrease. Statement I says it increases, so Statement I is false.
2. Analysis of Statement II: From the formula \(v \propto \frac{1}{n}\), velocity is inversely proportional to the principal quantum number. Therefore, if the principal quantum number \(n\) decreases, the magnitude of velocity increases. Statement II is true.
Step 4: Final Answer:
Statement I is false but Statement II is true.