**Problem Statement:**Calculate the uncertainty of the radius of the electron in the 1s wavefunction (i.e., ⟨Δr⟩).**Explanation:**This problem asks us to determine the uncertainty (⟨Δr⟩) in the radial position of an electron when it is in the 1s state of a hydrogen-like atom, using quantum mechanics principles. This involves calculating the expected value of the radial position and its fluctuation using the wavefunction associated with the 1s orbital.**Further Exploration:**1. **Understanding the 1s Wavefunction:** - The 1s orbital represents the lowest energy state of an electron in a hydrogen atom. - The wavefunction describes the probability distribution of the electron's position.2. **Mathematical Framework:** - The uncertainty is calculated using the standard deviation of the radial position. - This involves integrals over probability densities derived from the wavefunction.**Applications:**This calculation is critical for understanding quantum uncertainty in atomic systems and plays a fundamental role in quantum mechanics and chemistry education.

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