Question

An LED that emits light of wavelength λ = 614 nm illuminates the phototube. A reverse bias is applied to the phototube (a voltage that opposes the current flow). This is adjusted carefully until the photocurrent drops to zero. The stopping potential is found to be Vo = 0.162 V.

The LED can now be changed and the process repeated for a different λ. Then the data can be plotted to determine Planck's constant, h.

For the data collected above what value would you plot on the x-axis of your graph? (Use c = 3.00 x 108m/s.)

Express your answer in SI units to 3 significant figures.

Entering numbers in scientific notation: Example: 1.45 x 10-9 should be entered as 1.45E-9

Answer 1

Here, we shall be applying the following relations, we know that the energy or work function W can be expressed as

with e is the charge on the electron and V0 is the stopping potential. The other expression for energy can be expressed as

nu is the frequency and h is the Plank's constant, lambda is the wavelength, respectively.

At stopping potential , Eq. (1) and Eq. (2) balances and can be shown as

Clearly, the above is the equation of straight line with slope (h/e) and intercept at zero. So if we plot a graph by taking Vo along x axis and we will take frequency nu along x axis then by evaluating the slope we can get the value of Plank's constant h. Firstly for the known value of lambda we will find the frequency as follows (by using Eq. (2)

From the figure, the slope m comes out to be

So h can be calculated as

The above can be written as 5.6 E-34