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"When a metal is irradiated with radiation of suitable frequency, photo electrons are ejected from it, making the metal (slightly) positively charged. So more energy is required to eject more electrons from the same metal. Hence the the work function should increase"

Please mention any flaw in the above paragraph.

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Well, if the metal is connected to something else (as it is in most experiments, often to ground) then the induced charge will pull electrons from ground, which will restore the neutral state.

If the metal is completely isolated, then yes, you will induce some charge, but it's important to keep an eye on the significance: that charge is diluted over a macroscopically-sized sample, and in most cases it will result in a negligible change in the work function. In less-realistic cases, if you just keep going and going, then yes, the work function will start some meaningful increase at some point.

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