Assertion (A) : In an atom, the velocity of electron in the higher orbits keeps on decreasing
Reason (R ) : Velocity of electron in inversely proportional to the radius of the orbit

Options

A. If both (A) and (R ) correct and (R ) is the correct explanation for (A)
B. If both (A) and (R ) correct and (R ) is the correct explanation for (A)
C. If (A) is correct but (R ) is incorrect
D. If (A) is incorrect but (R ) is correct

Explanation

To solve the assertion-reason question, we will analyze both the assertion (A) and the reason (R) step by step.

### Step 1: Understand the Assertion (A)
The assertion states: "In an atom, the velocity of electron in the higher orbits keeps on decreasing."

- **Explanation**: In atomic physics, as we move to higher energy levels (orbits), the principal quantum number (n) increases. The formula for the velocity (v) of an electron in a given orbit is given by:

\[ v = 2.8 \times 10^6 \times \frac{Z}{n} \]

where Z is the atomic number and n is the principal quantum number (orbit number). As n increases, the velocity v decreases.

### Step 2: Understand the Reason (R)
The reason states: "Velocity of electron is inversely proportional to the radius of the orbit."

- **Explanation**: The relationship between the velocity of an electron and the radius of its orbit can be derived from Coulomb's law and Newton's second law. The centripetal force required to keep an electron in orbit is provided by the electrostatic force of attraction between the nucleus and the electron.

From the equations of motion, we have:

\[ F = \frac{K \cdot Z \cdot e^2}{R^2} \quad \text{(Coulomb's Law)} \]

and

\[ F = \frac{mv^2}{R} \quad \text{(Centripetal Force)} \]

Setting these equal gives:

\[ \frac{mv^2}{R} = \frac{K \cdot Z \cdot e^2}{R^2} \]

Rearranging this leads to:

\[ v^2 = \frac{K \cdot Z \cdot e^2}{mR} \]

Thus, we can see that \( v^2 \) is inversely proportional to R, which implies that as the radius increases, the velocity decreases.

### Step 3: Conclusion
Both the assertion and the reason are correct. Furthermore, the reason correctly explains the assertion.

### Final Answer
- **Assertion (A)**: True
- **Reason (R)**: True
- **Explanation**: The reason is the correct explanation for the assertion.

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