Question

Which of the following is the correct plot for the probability density ψ²(r) as a function of distance ‘r’ of the electron from the nucleus for 2s orbital?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

To determine the correct plot for the probability density \( \psi^2(r) \) as a function of the distance 'r' for the 2s orbital of an electron, let's analyze the characteristics of the 2s orbital in quantum mechanics.

The 2s orbital is spherical in symmetry and has a characteristic radial distance, called a node, where the probability density becomes zero. For the 2s orbital, there is one radial node due to its principal quantum number being greater than one.

The probability density of an electron in a hydrogenic orbital is described by the square of its wave function, \( \psi^2 \). For a 2s orbital, the plot of \( \psi^2(r) \) against 'r' typically starts at zero when \( r = 0 \), increases to a maximum, decreases to zero at the node, increases again to a peak representing the most probable distance, and then decreases as 'r' tends to infinity.

From the options given, we need to identify which plot matches these characteristics: starting at zero, showing a peak, reaching zero at a node, showing another peak, and then approaching zero.

Correct plot for \( \psi^2(r) \) of a 2s orbital.

As per the given options and their analysis, the correct plot for \( \psi^2(r) \) as a function of distance 'r' of the electron from the nucleus for a 2s orbital is the image with data-src-id="65acedd56e0d11a4f6287456". This plot appropriately shows a behavior consistent with the discussed characteristics of the probability density for a 2s orbital.