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?
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a
λe increases at the same rate as λph for λph
b
λedecreases with increases in ϕand λph
c
λeis approximately halved, if d is doubled
d
For large potential difference (v>>ϕ/e), λe is approximately halved if V made four times
answer is D.
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Detailed Solution
K.E of electron just after ejection =hcλph-ϕK.E of electron when it reaches anode =Kmax=hcλph-ϕ+Ve minimum de Broglie wavelength λe=h2Kmaxmλe=h2hcλph-ϕ+Vem Given that Ve >>ϕ (hcλph is also small for visible light)∴λeα1V ⇒ when V is made 4 times, λe will be halved.