Assertion (A) : The radial probability of` 1s` electrons first increases,till it is maximum at `0.53 Å` and then decreases to zero
Reason (R ) : Bohr's radius for the first is `0.53 Å`

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 given question, we will analyze the assertion and the reason step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the radial probability of 1s electrons first increases until it reaches a maximum at 0.53 Å and then decreases to zero.
- This is based on the concept of radial probability density, which describes the likelihood of finding an electron at a certain distance from the nucleus.

2. **Understanding the Reason (R)**:
- The reason states that Bohr's radius for the first electron shell (1s) is 0.53 Å.
- Bohr's model of the atom provides the radius for the electron's orbit in the hydrogen atom, where the first shell corresponds to the 1s orbital.

3. **Graphical Representation**:
- To visualize this, we can plot a graph where the x-axis represents the distance from the nucleus (r) and the y-axis represents the radial probability density.
- The graph starts at zero, increases to a maximum value at 0.53 Å, and then decreases back to zero. This behavior confirms the assertion.

4. **Evaluating the Statements**:
- Both the assertion and the reason are correct:
- The assertion accurately describes the behavior of radial probability for 1s electrons.
- The reason correctly identifies Bohr's radius for the first electron shell as 0.53 Å.

5. **Determining the Relationship**:
- Although both statements are correct, the reason (R) does not provide a direct explanation for the assertion (A). The assertion discusses the behavior of radial probability, while the reason states a fact about Bohr's radius without explaining why the radial probability behaves that way.

6. **Conclusion**:
- Therefore, the correct conclusion is that both A and R are correct, but R is not the correct explanation of A.

### Final Answer:
- The correct option is: Both A and R are correct, but R is not the correct explanation of A.