The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v0 is thrshold frequency] :

Question

The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v0 is thrshold frequency] : (A) λ propto (1/(v-v0)(3)2) (B) λ propto (1/(v-v0)(1)2) (C) λ propto (1/(v-v0)(1)4) (D) λ propto (1/(v-v0) )

Tardigrade Admin · Accepted Answer

For electron λDB = (λ/√2mK.E.) (de broglie wavelength) By photoelectric effect hv = hv0 + KE KE = hv - hv0 λDB =(h/√2m×(hv -hv0)) λDB propto (1/(v-v0)(1)2 )

Q. The de Broglie wavelength $(λ)$ associated with a photoelectron varies with the frequency (v) of the incident radiation as, [ $v_{0}$ is thrshold frequency] :

$λ \propto \frac{1}{( v - v _{0} ) ^{\frac{3}{2}}}$

$λ \propto \frac{1}{( v - v _{0} ) ^{\frac{1}{2}}}$

$λ \propto \frac{1}{( v - v _{0} ) ^{\frac{1}{4}}}$

$λ \propto \frac{1}{( v - v _{0} )}$

For electron
$λ_{D B} = \frac{λ}{2 m K . E .}$ (de broglie wavelength)
By photoelectric effect
$h v = h v_{0} + K E$
$K E = h v - h v_{0}$
$λ_{D B} = \frac{h}{2 m \times ( h v - h v _{0} )}$
$λ_{D B} \propto \frac{1}{( v - v _{0} ) ^{\frac{1}{2}}}$

Q. The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v0​ is thrshold frequency] :

λ∝(v−v0​)23​1​

λ∝(v−v0​)21​1​

λ∝(v−v0​)41​1​

λ∝(v−v0​)1​