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CBSE Class 12 Physics 2017 Delhi Set 3 Paper

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Question : 3 of 8
Marks: +1, -0
An αα -particle and a proton are accelerated through the same potential difference. Find the ratio of their de Broglie wavelengths.
Solution:  
Finding the ratio of de Broglie wavelength
(  λα/λp)(\;{λ α}/{λ p})
λ=  h/p=  h/√2mK=  h/√2mqVλ=\;{h}/{p}=\;{h}/{{√{2 m K}}}=\;{h}/{{√{2 m q V}}}
∴  λα/λp=  h/√2mαqαV×  √2mpqpV/h∴ \;{λ α}/{λ p}=\;{h}/{{√{2 m_α q_α V}}} × \;{{√{2 m_p q_p V}}}/{h}
  λα/λp  =  √mpqp/√mαqα\;{λ_α}/{λ_p}\;=\;{{√{m_p q_p}}}/{{√{m_α q_α}}}
  =  √mpqp/√4mp2qp\;=\;{{√{m_p q_p}}}/{{√{4 m_p 2 q_p}}}
  =  1/2√2\;=\;{1}/{2 {√{2}}}
λα:λp  =1:2√2λ_α: λ_p\;=1: 2 {√{2}}
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