A proton when accelerated through a potential difference of V volt has a wavelength λ associated with it. An α - particle in order to have the same wavelength λ must be accelerated through a p.d. of
V/8 volt
V/4 volt
V volt
2V volt
A
V volt
B
2V volt
C
V/8 volt
D
V/4 volt
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Solution
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For proton, λp=0.286×10−10√νm where V is p.d For α−particle,λα=0.101×10−10√νm
so, keeping same α for proton and α−partside
1=λpλα=0.286×√Vα0.101×√VP
0.101×√VP=0.286×√Vα (0.101)2×VP=(0.286)2Vα
(0.101)2ν(0.286)2=Vα
(∵VP=V)
⇒Vα=V8volt
So, the answer is option (A).
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