The work functions of Aluminium and Gold are | vedclass

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(C) According to Einstein's photoelectric equation,the maximum kinetic energy of emitted photoelectrons is given by $K_{\max} = hf - \phi$,where $h$ i

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$1$

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(C) According to Einstein's photoelectric equation,the maximum kinetic energy of emitted photoelectrons is given by $K_{\max} = hf - \phi$,where $h$ is Planck's constant,$f$ is the frequency of incident radiation,and $\phi$ is the work function of the metal.Since $K_{\max} = eV_s$,where $V_s$ is the stopping potential,we can write: $eV_s = hf - \phi$.Rearranging this for the stopping potential,we get: $V_s = (h/e)f - (\phi/e)$.This equation is in the form of a straight line $y = mx + c$,where the slope $m = h/e$.Since $h$ (Planck's constant) and $e$ (charge of an electron) are universal constants,the slope of the stopping potential versus frequency plot is independent of the nature of the metal.Therefore,the slope for Gold and Aluminium is the same.The ratio of the slopes is $1:1$,which is $1$.

The work functions of Aluminium and Gold are $4.1\,eV$ and $5.1\,eV$ respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is $.......$

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