a proton and alpha particle is accelerated through the same potential which one of the two has
1) greater value of de-Broglie wavelength associated with it?
2) less kinetic energy?
 
 
 
 
 
 
 
 
 
 
 
 

Asked by modi72879 | 25th Nov, 2017, 11:29: AM

Expert Answer:

A proton and an a-particle are accelerated through the same potential. Which one of the two has
(i) greater value of de-Broglie wavelength associated with it and
(ii) less kinetic energy?
Give reasons to justify your answer.

 
Solution:
 
1) Using de-Broglie wavelength formula, we already know that proton and alpha particle are accelerated through the same potential.
So, both their velocities are same.
begin mathsize 12px style straight lambda equals fraction numerator straight h over denominator square root of 2 mV subscript straight o straight q end root end fraction
so comma
straight lambda space straight alpha space fraction numerator 1 over denominator square root of mq end fraction
straight lambda subscript straight alpha over straight lambda subscript straight p equals square root of fraction numerator straight m subscript straight p straight q subscript straight p over denominator straight m subscript straight a straight q subscript straight a end fraction end root

charge space on space alpha space particle space equals space 2 space straight x space charge space on space proton
Also comma space mass space of space alpha space particle space equals space 4 space straight x space mass space of space proton
straight lambda subscript straight alpha over straight lambda subscript straight p equals fraction numerator 1 over denominator 2 square root of 2 end fraction
straight lambda subscript straight p equals space 2 square root of 2 space straight lambda subscript straight alpha
end style
Therefore, proton has a greater de-Broglie wavelength than the alpha particle.
 
2) For same potential of acceleration, K.E is directly proportional to the 'q'
As, the charge of an alpha particle is more than the proton,
hence proton has a lesser value of Kinetic Energy (K.E)

Answered by Abhijeet Mishra | 25th Nov, 2017, 11:27: PM