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Two light sources are used in a photoelectric experiment to determine the work function for a particular metal surface. When green light from a mercury lamp (λ=546.1\lambda = 546.1 nm) is used, a stopping potential of 0.376 V reduces the photocurrent to zero. What stopping potential would be observed when using the yellow light from a helium discharge tube (λ=587.5\lambda = 587.5 nm)?

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From the problem 14(a)\textit{14(a)}, we know work function of the metal is ϕ=1.90eV\phi=1.90\textrm{eV}. Thus, for the photoelectron wavelength of λ=587.5nm\lambda=587.5\textrm{nm}, we know that the maximum kinetic energy equation states:

K.Emax=e[V]=hcλϕ\begin{align*} K.E_{max}=\textrm{e}\left[\triangle{V}\right]=\frac{h\textrm{c}}{\lambda}-{\phi} \end{align*}

Hence, we calculate maximum kinetic energy of the ejected electrons as:

K.Emax=6.63×1034Js(3×108ms)587.5×109m[1eV1.6×1019J]1.90eV\begin{align*} K.E_{max}=\frac{6.63\times10^{-34}\textrm{J}\cdot{s}\left(3\times10^{8}\frac{\textrm{m}}{\textrm{s}}\right)}{587.5\times10^{-9}\textrm{m}}\left[\frac{1\textrm{eV}}{1.6\times10^{-19}\textrm{J}}\right]-1.90\textrm{eV} \end{align*}

Solution is:

K.Emax=0.216eV\begin{align*} \boxed{K.E_{max}=0.216\textrm{eV}} \end{align*}

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