To analyze the scenario of a neutron colliding with a stationary hydrogen atom in its ground state, we need to consider the principles of collision types and energy levels in quantum mechanics. Let's break down each statement to determine its validity.
Understanding the Collision Types
Collisions can be classified as elastic or inelastic. In an elastic collision, both momentum and kinetic energy are conserved, while in an inelastic collision, momentum is conserved, but kinetic energy is not. A perfectly inelastic collision is a specific case where the colliding bodies stick together after the collision.
Evaluating Each Statement
- a) If the kinetic energy of the neutron is less than 13.6 eV, the collision must be elastic.
This statement is false. While a kinetic energy less than 13.6 eV indicates that the neutron does not have enough energy to excite the hydrogen atom to a higher energy state, it does not guarantee that the collision is elastic. The neutron could still transfer some energy to the hydrogen atom, resulting in an inelastic collision.
- b) If the kinetic energy of the neutron is less than 13.6 eV, the collision may be inelastic.
This statement is true. Since the neutron's energy is insufficient to excite the hydrogen atom, it can still collide and transfer some of its kinetic energy to the atom, leading to an inelastic collision. The neutron may lose some energy without causing an excitation.
- c) Inelastic collision may take place when the initial kinetic energy of the neutron is greater than 13.6 eV.
This statement is also true. If the neutron has more than 13.6 eV of kinetic energy, it can excite the hydrogen atom to a higher energy state or even ionize it, depending on the energy level. Thus, inelastic collisions can occur when the neutron has sufficient energy to interact with the atom's electrons.
- d) Perfectly inelastic collision cannot take place.
This statement is false. A perfectly inelastic collision can occur if the neutron collides with the hydrogen atom and they stick together after the collision. However, this scenario is less likely due to the nature of neutrons and hydrogen atoms, but it is not impossible.
Summary of Findings
In summary, the true statements regarding the collision of a neutron with a stationary hydrogen atom in its ground state are:
- Statement b is true: The collision may be inelastic if the neutron's kinetic energy is less than 13.6 eV.
- Statement c is true: Inelastic collisions can occur when the neutron's kinetic energy exceeds 13.6 eV.
On the other hand, statements a and d are false. Understanding these principles helps clarify how energy transfer and quantum states interact during collisions at the atomic level.
