Dual Nature of Matter

JEE Main level, single correct, medium

131 of 200

Question 131 of 200

The work functions of Aluminium and Gold are 4.1eV4.1eV and 5.1eV5.1eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

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Answer: (C) 11

The data given is
ϕAl=4.1eV{\phi }_{Al}=4.1eV
ϕAu=5.1eV{\phi }_{Au}=5.1eV
The energy is given by
hν=ϕ+KE⇒hν=ϕ+eV0h\nu =\phi +KE \Rightarrow h\nu =\phi +e{V}_{0}
where V0{V}_{0} is the stopping potential and K=eV0K=e{V}_{0}
Thus, the above equation can be written as
eV0=hν−ϕe{V}_{0}=h\nu -\phi
⇒V0=hνe−ϕe\Rightarrow {V}_{0}=\dfrac{h\nu }{e}-\dfrac{\phi }{e}
The equation is of the form of y=mx+cy=mx+c. The slope is
m=hem=\dfrac{h}{e}.
Since the Planck constant hh and charge of an electron is a constant ee, the slope does not depend on the work function. Hence the ratio of the slope of the plot of stopping potential and frequency for both the given metals is 11.

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