1. Tardigrade
  2. Question
  3. Physics
  4. When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TA eV and de-Broglie wavelength λA. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is TB = (TA - 1.5)eV . If the de-Broglie wavelength of these photoelectrons λB = 2λA, then the work function of metal B is :

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Q. When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy $T_A$ eV and de-Broglie wavelength $\lambda_{A}$. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is $T_B = (T_A - 1.5)$eV . If the de-Broglie wavelength of these photoelectrons $\lambda_{B} = 2\lambda_{A},$ then the work function of metal B is :

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Solution:

$\lambda_{B}=2\lambda_{A}$
$\Rightarrow \frac{h}{\sqrt{2T_{B}m}}=\frac{2h}{\sqrt{2T_{A}m}}$
$T_{A}=4T_{B}\,...\left(i\right)$
and $T_{B} = \left(T_{A}- 1.5\right) eV\,...\left(ii\right)$
from $\left(i\right)$ and $\left(ii\right)$
$3T_{B}\,1.5\,eV \Rightarrow T_{B}=0.5\,eV$
$T_{B}=0.5\,eV=4.5\,eV-\phi_{B}$
$\phi=4\,eV$