JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
The de Broglie wavelength associated with an electron accelerated through a potential difference V is \(\lambda_e\) and the de Broglie wavelength associated with a proton accelerated through the same potential difference is \(\lambda_p\). If their corresponding masses are \(m_e\) and \(m_p\), respectively, then the ratio of their de Broglie wavelengths \(\left(\dfrac{\lambda_e}{\lambda_p}\right)\) is ______.
- A \(\sqrt{\dfrac{m_p}{m_e}}\)
- B \(\sqrt{\dfrac{m_e}{m_p}}\)
- C \(\dfrac{m_p}{m_e}\)
- D \(\left(\dfrac{m_p}{m_e}\right)^2\)
Answer & Solution
Correct Answer
(A) \(\sqrt{\dfrac{m_p}{m_e}}\)
Step-by-step Solution
Detailed explanation
The de Broglie wavelength of a particle accelerated through a potential difference \(V\) is given by \(\lambda = \dfrac{h}{\sqrt{2mqV}}\). For an electron, the charge is \(e\) and mass is \(m_e\). Its de Broglie wavelength is \(\lambda_e = \dfrac{h}{\sqrt{2m_e eV}}\). For a…
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