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The graph shows the variation of stopping potential with frequency of incident radiation for two photosensitive metals A and B. Which one of the two has higher value of work-function? Justify your answer.

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To determine which of the two photosensitive metals, A or B, has a higher value of the work function, we need to analyze their respective graphs showing the variation of stopping potential (VsVs) with frequency (ff) of incident radiation. The work function (WW) of a metal is the minimum energy required...
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To determine which of the two photosensitive metals, A or B, has a higher value of the work function, we need to analyze their respective graphs showing the variation of stopping potential (VsVs) with frequency (ff) of incident radiation.

The work function (WW) of a metal is the minimum energy required to remove an electron from the surface of the metal and is directly related to the threshold frequency (f0f0) by the equation:

W=hf0W=hf0

where:

  • WW is the work function,
  • hh is Planck's constant (6.626×10−34 J⋅s6.626×10−34J⋅s),
  • f0f0 is the threshold frequency.

From the graph, the stopping potential (VsVs) is directly proportional to the frequency (ff) of the incident radiation and is given by the equation:

Vs=hfe−WeVs=ehfeW

where:

  • VsVs is the stopping potential,
  • ff is the frequency of the incident radiation,
  • ee is the elementary charge (1.602×10−19 C1.602×10−19C),
  • WW is the work function.

By analyzing the graph, we can observe the following:

  1. The slope of the graph represents the ratio heeh, which is constant.
  2. The intercept on the VsVs axis represents −We−eW, the negative of the work function divided by the elementary charge.

Since the work function is proportional to the intercept, the metal with the higher stopping potential (i.e., the metal with the higher intercept on the VsVs axis) has a higher work function.

Therefore, in the given graph, the metal associated with the higher stopping potential (further above the x-axis) has the higher value of the work function.

 
 
 
 
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