The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (ν) of the incident radiation as, [ν0 is threshold frequency]

Engineering

Chemistry

Dual Behaviour and de Broglie Hypothesis

Question

The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (ν) of the incident radiation as, [ν₀ is threshold frequency]

$λ \propto \frac{1}{{(ν - ν_{0})}^{\frac{1}{2}}}$

$λ \propto \frac{1}{(ν - ν_{0})}$

$λ \propto \frac{1}{{(ν - ν_{0})}^{\frac{3}{2}}}$

$λ \propto \frac{1}{{(ν - ν_{0})}^{\frac{1}{4}}}$

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$λ = \frac{h}{mv}$

According to Einstein’s theory of photoelectric effect:

hν = hν₀ + KE

$hν = {hν}_{o} + \frac{1}{2} {mv}^{2}$

2h(ν – ν₀) = mv²

$\frac{2 h (ν - ν_{0})}{m} = v^{2}$

$v \propto {(ν - ν_{o})}^{\frac{1}{2}}$

$λ \propto \frac{h}{m {(ν - ν_{o})}^{\frac{1}{2}}}$

$λ \propto \frac{1}{{(ν - ν_{o})}^{\frac{1}{2}}}$