Q114 / 125 · BITSAT 2018 · Physics

When photon of energy 4.0 eV strikes the surface of a metal A, the elected photoelectrons have maximum kinetic energy TA eV and de-Broglie wavelength λA. The maximum kinetic energy of photoelectron liberated from another metal B by photon of energy 4.50 eV is TB=TA-1.50 eV. If the de-Broglie wavelength of these photoelectrons λB=2λA, then choose the correct statement(s).

  • A
    The work function of A is 1.50 eV
  • Correct answer
    B
    The work function of B is 4.0 eV
  • C
    TA=3.2 eV
  • D
    All of the above

Solution

From Einstein photoelectric equation,
E=ϕ0+KEmax

For metal A  4=ϕA+TA....i
For metal B 4.5=ϕB+TA-1.5....ii

From Eq. (i) and (ii), wo got
ϕB-ϕA=2

Now, according to de-Broglie hypothesis,
λA=hmv=h2mTA

Similarly, λB=h2mTB

∴ λAλB=TBTA=TA-1.5TA=1-1.5TA1/2

122=1-1.5TA

On solving, TA=2.0eV

or ϕA=4-TA=4-2=2.0eV

ϕB=6-TA=6-2=4.0eV

Hence, the correct answer is option: 'B'.

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