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?

Engineering

Physics

Photoelectric Effect Einsteins Equation

de Broglie Hypothesis and Dual Nature

Question

Light of wavelength λ_ph 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 λ_e, which of the following statement(s) is(are) true?

λ_e is approximately halved, if d is doubled

λ_e decreases with increase in $ϕ$ and λ_ph

For large potential difference (V >> $ϕ$ /e), λ_e, is approximately halved if V is made four times

λ_e increases at the same rate as λ_ph for λ_ph < hc/ $ϕ$

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$λ_{e} = \frac{h}{p} = \frac{h}{\sqrt{2 km}} = \frac{h}{\sqrt{2 {(\frac{hc}{λ_{0}} - φ + eV)}^{m}}}$