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

[rushil]

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 $$\triangle E$$. 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?

 

[jtbell]

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.

 

[rushil]

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!