Light of wavelength λ p h falls on a cathode plate inside a vacuum tube as shown in the figure. The work…

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 ?

  1. For large potential difference V ϕ e , λ e is approximately halved if V is made four times
  2. λ e increases at the same rate as λ ph for λ ph < hc ϕ
  3. λ is approximately halved, if d is doubled
  4. λ decreases with increase in ϕ and λ ph

Solution

Kmax=hcλPh-ϕ
Kinetic energy of e- reaching the anode will be
K=hcλPh-ϕ+eV
Now λe=h2mK=h2mhcλPh-ϕ+eV
If eVϕ
λe=h2mhcλPh+eV
If Vf=4Vi
λefλei2

Asked in: JEE Advanced 2016 (Paper 2)

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