Class 12 NEET Physics Dual Nature of Matter and Radiation

Wavelength of an electron of energy E is
λe=

h

√2meE

.............(i)
Wavelength of a photon of same energy E is
λp=

hc

E

or E=

hc

λp

.............(ii)
Squarin both sides of Eq. (i), we get
λe2=

h2

2meE

or E=

h2

2meλe2

.............(ii)
Equating (ii) and (iii), we get

hc

λp

=

h2

2meλe2

λp=

2mec

h

λe2
λp∝λe2