The de Broglie wavelength associated with an electron accelerated through a potential difference V is _e and the de Broglie wavelength associated with a proton accelerated through the same potential difference is _p . If their corresponding masses are m_e and m_p , respectively, then the ratio of their de Broglie wavelengths ( _e _p ) is ______.

Step-by-step solution

The de Broglie wavelength of a particle accelerated through a potential difference V is given by = h 2mqV . For an electron, the charge is e and mass is m_e . Its de Broglie wavelength is _e = h 2m_e eV . For a proton, the charge is e and mass is m_p . Its de Broglie wavelength is _p = h 2m_p eV . Taking the ratio of the two wavelengths, we get _e _p = h 2m_e eV h 2m_p eV = m_p m_e . Answer: m_p m_e