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

We need the ratio of slopes of stopping potential vs frequency plots for Gold and Aluminium.

State the photoelectric equation.

Einstein's photoelectric equation: $$eV_0 = h\nu - \phi$$

$$V_0 = \dfrac{h}{e}\nu - \dfrac{\phi}{e}$$

Identify the slope.

The slope of $$V_0$$ vs $$\nu$$ plot is $$\dfrac{h}{e}$$, which is a universal constant independent of the material.

Therefore, the ratio of slopes = $$\dfrac{h/e}{h/e} = 1$$.

This corresponds to Option 3.