JEE Advanced2016PhysicsDual Nature of MatterActual
Light of wavelength λ p h 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)
Options
- AFor large potential difference V ≫ ϕ e , λ e is approximately halved if V is made four times
- Bλ e increases at the same rate as λ ph for λ ph < hc ϕ
- Cλ ⅇ is approximately halved, if d is doubled
- Dλ ⅇ decreases with increase in ϕ and λ ph
Correct answer
A. For large potential difference V ≫ ϕ e , λ e is approximately halved if V is made four times
Step-by-step solution
K m a x = h c λ P h - ϕ Kinetic energy of e - reaching the anode will be K = h c λ P h - ϕ + e V Now λ e = h 2 m K = h 2 m h c λ P h - ϕ + e V If e V ≫ ϕ λ e = h 2 m h c λ P h + e V If V f = 4 V i λ e f ≃ λ e i 2