Q.

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.
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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?