I think the following question which appeared in a Medical Entrance question paper will confuse the students:
If the kinetic energy of the particle is increased by 16 times, the percentage change in the de Broglie wave length of the particle is
(a) 25% (b) 75% (c) 60% (d) 50% (e) 30%
The answer given to this question is 75%. In multiple choice questions, the most suitable choice need be picked out and indeed the answer then is 75%. The answer will be exactly 75% if you mean that the final kinetic energy of the particle is 16 times the initial kinetic energy, as shown below:
Kinetic energy, E = p2/2m where ‘p’ is the linear momentum and ‘m’ is the mass. If E is increased to 16 times the initial value, ‘p’ is increased to 4 times the initial value. Since de Broglie wave length λ = h/p where ‘h’ is Planck’s constant, the final wave length will be λ/4. The percentage change in the wave length is therefore 75%.
If the kinetic energy is increased by 16 times as stated in the question, the final kinetic energy will be 17 times the initial kinetic energy and the final momentum will be 4.123 times the initial momentum. The final wave length will be 0.243 times the initial wave length and the percentage change in the wave length will be 75.5%.
In the present question, the answers are almost the same. But suppose the words ‘increased by 16 times’ were replaced by ‘increased by 4 times’. The difference between the answers will be significant. If you mean that the final energy is 4 times, you should modify the words as ‘increased to 4 times’ or ‘made 4 times’. I thought of posting this because I have seen this type of confusing wording in many instances.
If the kinetic energy of the particle is increased by 16 times, the percentage change in the de Broglie wave length of the particle is
(a) 25% (b) 75% (c) 60% (d) 50% (e) 30%
The answer given to this question is 75%. In multiple choice questions, the most suitable choice need be picked out and indeed the answer then is 75%. The answer will be exactly 75% if you mean that the final kinetic energy of the particle is 16 times the initial kinetic energy, as shown below:
Kinetic energy, E = p2/2m where ‘p’ is the linear momentum and ‘m’ is the mass. If E is increased to 16 times the initial value, ‘p’ is increased to 4 times the initial value. Since de Broglie wave length λ = h/p where ‘h’ is Planck’s constant, the final wave length will be λ/4. The percentage change in the wave length is therefore 75%.
If the kinetic energy is increased by 16 times as stated in the question, the final kinetic energy will be 17 times the initial kinetic energy and the final momentum will be 4.123 times the initial momentum. The final wave length will be 0.243 times the initial wave length and the percentage change in the wave length will be 75.5%.
In the present question, the answers are almost the same. But suppose the words ‘increased by 16 times’ were replaced by ‘increased by 4 times’. The difference between the answers will be significant. If you mean that the final energy is 4 times, you should modify the words as ‘increased to 4 times’ or ‘made 4 times’. I thought of posting this because I have seen this type of confusing wording in many instances.
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