If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is

Question

If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is (A)  c√(2m/E)  (B)  √(2m/E)  (C)  √(2m/cE)  (D)  √(m/E)

Tardigrade Admin · Accepted Answer

Energy, E=(hc/λ p) or λ p=(hc/E) and λ e=(h/p)=(hc/√2mE) ∴ (λ p/λ e)=(E/(h)√2mE) or (λ p/λ e)=(c√2mE/E)=c√(2m/E)

Q. If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is

$c \frac{2 m}{E}$

$\frac{2 m}{E}$

$\frac{2 m}{c E}$

$\frac{m}{E}$

$\frac{c m}{E}$

Energy, $E = \frac{h c}{λ _{p}}$
or $λ_{p} = \frac{h c}{E}$ and $λ_{e} = \frac{h}{p} = \frac{h c}{2 m E}$
$∴$ $\frac{λ _{p}}{λ _{e}} = \frac{E}{\frac{h}{2 m E}}$
or $\frac{λ _{p}}{λ _{e}} = \frac{c 2 m E}{E} = c \frac{2 m}{E}$

Q. If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is

cE2m​​

E2m​​