Dual Nature of Matter

JEE Main level, single correct, medium

178 of 200

Question 178 of 200

The surface of certain metal is first illuminated with light of wavelength λ1=350nm{\lambda }_{1}=350nm and then, by a light of wavelength λ2=540nm.{\lambda }_{2}=540nm. It is found that the maximum speed of the photoelectrons in the two cases differ by a factor of 22. The work function of the metal (in eVeV) is close to

(Energy of photon =1240λ(innm)eV=\dfrac{1240}{\lambda \left(innm\right)}eV )

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Answer: (B) 1.81.8

λ1=350nm,λ2=540nm,V1V2=2⇒V1=2VandV2=V{\lambda }_{1}=350nm, {\lambda }_{2}=540 nm, \dfrac{{V}_{1}}{{V}_{2}}=2\Rightarrow {\text{V}}_{1}=2\text{V}and{\text{V}}_{2}=V

hcλ1=ϕ+12m(2V)2\dfrac{hc}{{\lambda }_{1}}=\phi +\dfrac{1}{2}m{\left(2V\right)}^{2}

hcλ2=ϕ+12mV2\dfrac{hc}{{\lambda }_{2}}=\phi +\dfrac{1}{2}m{V}^{2}

hcλ1−4hcλ2=ϕ−4ϕ\dfrac{hc}{{\lambda }_{1}}-4\dfrac{hc}{{\lambda }_{2}}=\phi -4\phi

hc(4540−1340)=3ϕhc\left(\dfrac{4}{540}-\dfrac{1}{340}\right)=3\phi

ϕ=1.8eV\phi =1.8eV

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