An electron of mass m_e and a proton of mass m_p = 1836 m_e are moving with the same speed. The ratio of their de Broglie wavelength $${{{}^\lambda electron} \over {{}^\lambda proton}}$$ will be :

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is :

An $$\alpha$$ particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are $$\lambda$$_$$\alpha$$ and $$\lambda$$_p respectively. The ratio $${{{{\lambda _p}} \over {{\lambda _\alpha }}}}$$ is :

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :