The Question is from neet-physics nuclei , and it was created by the author VENKATESWARARAO

Question

An electron with kinetic energy $5\,\,eV$ is incident on a $H$-atom in its ground state. The collision

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Energy quantization in atoms and collision types
	**Related Topics**: Atomic energy levels, electron-atom collisions, elastic and inelastic collisions.
	**Prerequisites**: Understanding of atomic structure, quantized energy levels, and collision mechanics.
## SOLUTION PATHWAY
**Given Information**:
	* Electron kinetic energy = 5 eV
	* Hydrogen atom in its ground state
**Method & Steps**:
	1.  Determine the energy required for the first excitation of hydrogen.
		Reasoning: Hydrogen's first excitation requires energy to move an electron to the n=2 level.
		Formula/Rule: The energy of the nth level in hydrogen is given by $E_n = -13.6/n^2$ eV. The first excitation energy is $E_2 - E_1 = -13.6/4 - (-13.6) = 10.2$ eV
	2. Compare the incident electron's energy with the hydrogen's excitation energy.
		Working: The electron's kinetic energy (5 eV) is less than the energy required for the first excitation (10.2 eV).
		Key Point: Since the electron does not have enough energy to excite the hydrogen atom, the collision must be elastic.
	3.  Conclude the collision type.
		Result: The collision must be elastic as the electron does not have enough energy to cause an electronic transition in the hydrogen atom.
		Verification: If the electron had at least 10.2eV, the collision could have been inelastic.
 ## OPTION ANALYSIS
[A] ✓: The collision must be elastic because the incident electron's kinetic energy is less than the energy required to excite the hydrogen atom to its first excited state. Therefore no energy can be transferred to internal energy of the atom.
[B] :x: Partially elastic collisions involve some energy transfer, but the electron does not have sufficient energy to cause any excitation.
[C] :x: The collision must be elastic and not completely elastic as the collision can not change the internal state of the hydrogen atom.
[D] :x: A completely inelastic collision would involve excitation of the hydrogen atom, which is not possible with the given energy of the electron.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Assuming any collision can be inelastic. [How to avoid]: Understand that inelastic collisions require sufficient energy to excite the atom.
		2. [Error 2]: Forgetting to consider the excitation energy of hydrogen. [How to avoid]: Remember that atoms have quantized energy levels.
	**Quick Tips**:
		1. [Helpful shortcut]: Quickly calculate the first excitation energy of Hydrogen as ~ 10.2 eV.
		2. [Memory aid]: Elastic collisions conserve kinetic energy; inelastic collisions involve energy transfer to internal states.

VENKATESWARARAO · Answer

The correct Option is "Must be elastic"

VENKATESWARARAO · Answer

May be partially elastic

VENKATESWARARAO · Answer

Must be completely elastic

VENKATESWARARAO · Answer

May be completely inelastic

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