Question 115: Dual Nature of Matter and Radiation

Question

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

Accepted Answer

We are given the work functions of Aluminium and Gold as $$4.1 ~\mathrm{eV}$$ and $$5.1 ~\mathrm{eV}$$, respectively.
The stopping potential ($$V_s$$) is related to the frequency ($$f$$) of the incident light by the equation:
$$eV_s = h(f - f_0)$$
Where $$e$$ is the charge of an electron, $$h$$ is Planck's constant, and $$f_0$$ is the threshold frequency. The threshold frequency is related to the work function ($$\phi$$) by:
$$\phi = hf_0$$
So, we can write the equation for stopping potential as:
$$V_s = \frac{h}{e}(f - \frac{\phi}{h})$$
This equation represents a straight line with slope $$\frac{h}{e}$$. Therefore, the slope of the stopping potential versus frequency plot is the same for both Aluminium and Gold. The ratio of the slopes is:
$$\frac{	ext{Slope for Gold}}{	ext{Slope for Aluminium}} = \frac{\frac{h}{e}}{\frac{h}{e}} = 1$$
So , the ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is 1.

Answer

1.5

Answer

1.24

Answer

1

Answer

2

Dual Nature of Matter and Radiation

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

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