Hi could someone explain how to 2014 HSC Q26 b)? I completely don't understand the working out provided in the answer especially since I've never done calculations where there's a non-zero voltage across the electrodes for the photoelectric effect.
Thanks in advance! (also how do you upload images on posts? do you have to upload them to imgur first?)
Hey Cindy!
No problems! A conceptually difficult question on the stopping voltage experiment here, requires a bit of calculations as well! What's so difficult about it are two things:
1. Understanding the significance of stopping voltage and maximum kinetic energy
2. Applying and understanding the formula E=qV
Here at Atarnotes we want the best for our students, so I will hold your hand through this.The diagram of the experiment indicates 4.1V as the stopping voltage, which is the point at which the voltage source provides enough energy to repel the ejected electron so that it doesnt reach the anode (or collector) and hence no current will be detected. The point of having a stopping voltage is just so that we can work out the work function, which is the minimum energy required to eject electrons from a metal.
I will prove to you why this is the case:
Maximum kinetic energy = hf - work function _____ equation 1This is the equation for calculating the kinetic energy of ejected electrons as a light beam shines upon the metal.
But since stopping voltage works against the motion of electrons:
Maximum kinetic energy = hf - qV ________ equation 2Hence by balancing equation 2 and equation 1, we can see that work function = qV
So work function of the metal = 4.1eV
Good good, now the difficult part is over, congratulations.
We need to do two things for this question
1. Draw the line on the graph for the experiment done with 0.0VTo draw the line, we must know its x-intercept, which is the threshold frequency. We can calculate threshold frequency through the formula:
Work function = planck's constant x threshold frequencyWe know work function = 4.1eV = 4.1 x (1.602 x 10
-19)J
We know planck's constant = 6.632 x 10
-34Substitute in the values:
4.1 x (1.602 x 10-19)J = 6.632 x 10-34 x threshold frequencyHence threshold frequency of the metal = 9.9 x 10
14 Hz. So your line for the repeated experiment should have an x-intercept at 9.9. Now how can I draw this line without knowing another point? Easy, because we know that the gradient is always constant for kinetic energy versus frequency graphs because it is Planck's constant. So just draw your line with roughly the same gradient as the original line they have provided you with!
Moving onto the next part of the question:
2. Determine the radiation frequency which produces photoelectrons with maximum kinetic energy of 1.2eVRecall our formula:
Maximum kinetic energy = hf - work functionWe know that maximum kinetic energy as provided = 1.2eV = 1.2 x (1.602 x 10
-19)J
We know that work function = 4.1eV = 4.1 x (1.602 x 10
-19)J
And finally we know the value for h, which is Planck's constant
So now substitute all your values into the formula, and you obtain an answer of 1.3 x 10
15Hz as the radiation frequency
Very tough question, definitely a band 6 range response (only if there's a band 7). I hope my explanation helped!
Best Regards
Happy Physics Land