Verified Solution • 2025–26 Session moderate

QJEEM21Phb5db: JEE Main 2021 Physics - Class 12 JEEM21Phb5db Solution: An electron of mass m and a photon have same energy E. The…

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)

Multiple Choice Options

  • A 1c(2mE)1/2{1 \over c}{\left( {{{2m} \over E}} \right)^{1/2}}
  • B 1c(E2m)1/2{1 \over c}{\left( {{E \over {2m}}} \right)^{1/2}}
  • C (E2m)1/2{\left( {{E \over {2m}}} \right)^{1/2}}
  • D c(2mE)1/2c{(2mE)^{1/2}}

Step-by-Step Verified Solution

For photon, E = hcλ{{hc} \over \lambda }

λp=hcE{\lambda _p} = {{hc} \over E} .... (i)

For electron, λe=hc2mE{\lambda _e} = {{hc} \over {\sqrt {2mE} }} .... (ii)

λeλp=hc2mEhcE=E2mc2=1c(E2m)1/2{{{\lambda _e}} \over {{\lambda _p}}} = {{{{hc} \over {\sqrt {2mE} }}} \over {{{hc} \over E}}} = \sqrt {{E \over {2m{c^2}}}} = {1 \over c}{\left( {{E \over {2m}}} \right)^{1/2}}

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