JEE MAIN - Physics (2022 - 28th June Morning Shift - No. 14)
The de Broglie wavelengths for an electron and a photon are $$\lambda$$e and $$\lambda$$p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?
$${\lambda _p} \propto \lambda _e^2$$
$${\lambda _p} \propto {\lambda _e}$$
$${\lambda _p} \propto \sqrt {{\lambda _e}} $$
$${\lambda _p} \propto \sqrt {{1 \over {{\lambda _e}}}} $$
설명
$${\lambda _p} = {h \over p} = {{hc} \over E}$$ ...... (i)
$${\lambda _e} = {h \over {\sqrt {2mE} }}$$ ...... (ii)
From (i) and (ii)
$${\lambda _p} \propto \lambda _e^2$$