Quantum Mechanical Model Of Atom

Correct Answer: 3 × 10^-23 Kg·ms^-1

Explanation:
The momentum p of a photon is given by the formula:


Given:
• Planck’s constant
• Wavelength

Substituting into the formula:



Therefore, the momentum of the photon is 3 × 10^-23 Kg·ms^-1.

Step 1: Understanding and .
In quantum mechanics, the state of an electron in an atom is described by a wave function, represented by the Greek letter psi ( ). The wave function itself is a mathematical function (a solution to the Schrödinger equation) and does not have a direct physical meaning. However, its square, , does have a very important physical significance.
Step 2: Evaluating the Options.
(A) represents atomic orbit: An atomic orbital is the three-dimensional region of space around the nucleus where the probability of finding an electron is maximum (typically >90%). is the probability density at a single point, not the entire region (orbital). So, this is incorrect.
(B) Probability density of the electron at that point: According to Max Born's interpretation of the wave function, the value of at any given point in space is proportional to the probability of finding the electron at that point. More precisely, represents the probability of finding the electron in a small volume element dV. Therefore, is known as the probability density. This statement is correct.
(C) for nodes: A node is a point or a surface where the probability of finding an electron is zero. By definition, at a node, , and consequently, . This statement claims the opposite and is therefore incorrect.
(D) has no physical meaning: This is incorrect. As explained in (B), has a clear and crucial physical meaning: it represents the probability density of finding an electron. It is itself that has no direct physical meaning.
Step 3: Final Answer.
The correct statement is that represents the probability density of the electron at a point.