Light of wavelength λph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is ϕ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is λe, Which of the following $$statement(s)$$ $$is(are)true$$?

Question

Light of wavelength λph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is ϕ and  the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference  V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is  λe, Which of the following $$statement(s)$$ $$is(are)true$$?

Infinity Learn · Accepted Answer

K.E of electron just after ejection $$=hc$$λ$$ph-$$ϕK.E of electron when it reaches anode $$=Kmax=hc$$λ$$ph-$$ϕ$$+Ve$$   minimum de Broglie wavelength  λ$$e=h2Kmaxm$$λ$$e=h2hc$$λ$$ph-$$ϕ$$+Vem$$ Given that Ve  >>ϕ   (hc$$λph is also small for visible $$light)∴λeα$$1V$$ ⇒  when V is made $$4$$ times, λe will be halved.

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