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# The work function for a certain metal is $4.2 eV$. Will this metal give photoelectric emission for incident radiation of wavelength $589 nm$?

$\begin {array} {1 1} (a)\;Yes & \quad (b)\;No \\ (c)\;Maybe & \quad (d)\;Can't\: be\: determined \end {array}$

Ans : (b) No
$\phi_{\circ}=4.2eV$
$\lambda=589\: nm = 589 \times 10^{-9} m$
Energy of incident photon, $E = hc/ \lambda$
$= (6.626 \times 10^{-34} \times 3 \times 10^8 ) / 589 \times 10^{-9} = 3.33 \times 10^{-19} J/1.6 \times 10^{-19}$
$=2.08 eV$
It can be observed that the energy of the incident radiation is less than the work function of the metal. Hence, no photoelectric emission will take place.
edited Apr 2, 2014