Can Electrons Jump Between Energy Levels if the Energy is Not Precisely Matched?

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SUMMARY

Electrons in atoms exist in fixed, quantized energy states, and transitions between these states require precise energy matching, as defined by the energy difference, ΔE. In the case of a hydrogen atom, the energy differences between the first and second levels (13.6 eV) and the second and third levels (3.4 eV) illustrate this principle. If an incoming photon does not possess the exact energy required for a transition, the electron does not jump to a higher energy level; instead, it remains in its current state. In scenarios where the energy is slightly above or below the required threshold, the electron may briefly transition but will return to its original state almost instantaneously.

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  • Understanding of Quantum Mechanics principles
  • Familiarity with energy quantization in atomic physics
  • Knowledge of photon-electron interactions
  • Basic grasp of the hydrogen atom energy levels
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  • Study the concept of energy quantization in Quantum Mechanics
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rushil
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It's a well known fact from Quantum Mechanics that electrons exist in fixed, quantised energy states. Also, when they move from one energy level to another, they emit or absorb the energy as required by [tex]\triangle E[/tex]. Also, if a particular photon is absorbed , the apprpriate transition takes place. My question is regarding the second phenomenon. Suppose we consider a H atom s.t. the energy difference between 1st and 2nd energy levels is 13.6 eV and theat between 2nd and 3rd is 3.4 eV . What if we give Energy =
(i} 13.7 eV
(ii)13.3 eV
(iii) 4 eV... etc..??
Do electrons jump and then come back if the energy difference is not appropraite or do they just stay in position and don't jump if the PRECISE Energy is not provided?
 
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If the incoming photon does not have just the right energy to send an electron from its current energy state to a higher energy state, nothing happens.
 
Nothing happens... or the electron jumps but is not able to reach the required level and instantaneously returns... maybe this is so fast, our present equipments can't measure such a short time interval!
 

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