Question

Observe the given two statements about \(\alpha\)-particle experiment and Rutherford assumptions. Statement-I: The ratio of atomic radius to its nuclear radius is \(10^5\). Statement-II: In an atom, the majority of the space is vacant. The correct answer is

• A. Both statements I and II are correct
• B. Statement I is correct, but statement II is not correct
• C. Statement I is not correct, but statement II is correct
• D. Both statements I and II are not correct

Hint:

According to Rutherford's model, \[ \boxed{ \begin{aligned} &\text{Atomic radius}\approx10^{-10}\text{ m}, &\text{Nuclear radius}\approx10^{-15}\text{ m}. \end{aligned} } \] Thus, \[ \boxed{ \frac{\text{Atomic radius}}{\text{Nuclear radius}} =10^5, } \] showing that most of the atom is empty space.

Answer 1

The Correct Option is A

Step 1: Verify Statement-I. The atomic radius is approximately \[ 10^{-10}\text{ m}, \] while the nuclear radius is approximately \[ 10^{-15}\text{ m}. \] Therefore, \[ \frac{\text{Atomic radius}}{\text{Nuclear radius}} = \frac{10^{-10}}{10^{-15}} = 10^5. \] Hence, Statement-I is correct.

Step 2: Verify Statement-II. According to Rutherford's nuclear model, \[ \boxed{\text{Most of the mass is concentrated in the tiny nucleus,}} \] and therefore, \[ \boxed{\text{most of the volume of an atom is empty space}.} \] Hence, Statement-II is also correct.

Step 3: Write the conclusion. Both statements are correct. Hence, \[ \boxed{(A)} \] is the correct answer.