Q123 / 160 · JIPMER 2013 · Physics

The work function for metals $A, B$ and $C$ are respectively $1.92 \mathrm{eV}, 2.0 \mathrm{eV}$ and 5 eV. According to Einstein's equation the metals which will emit photo, electrons for a radiation of wavelength $4100 Å$ is/are

  • A
    none
  • B
    $A$ only
  • Correct answer
    C
    $A$ and $B$ only
  • D
    All the three metals

Solution

Work function for wavelength of $4100 Å$ is $\begin{aligned} W & =\frac{h c}{\lambda} \\ & =\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{4100 \times 10^{-10}} \\ & =4.8 \times 10^{-19} \mathrm{~J} \\ & =\frac{4.8 \times 10^{-19}}{1.6 \times 10^{-19}} \mathrm{eV} \\ & =3 \mathrm{eV}\end{aligned}$ Now, we have $\begin{aligned} & W_A=1.22 \mathrm{eV} \\ & W_B=2.0 \mathrm{eV} \\ & W_C=5 \mathrm{eV}\end{aligned}$ Since, $W_A \lt W$ and $W_B \lt W$, hence $A$ and $B$ will emit photoelectrons.

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

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