At what distance is the radial probability maximum for 1s orbital ? What is this distance called ?

Explanation

To find the distance at which the radial probability is maximum for the 1s orbital, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the 1s Orbital**: The 1s orbital is the simplest atomic orbital and is spherically symmetric around the nucleus. The probability density for finding an electron in this orbital varies with distance from the nucleus.

2. **Radial Probability Function**: The radial probability density is given by the function \( P(r) = |\psi(r)|^2 \times 4\pi r^2 \), where \( \psi(r) \) is the wave function of the electron in the 1s orbital, and \( r \) is the distance from the nucleus. This function accounts for the volume element in spherical coordinates.

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