Indirect Definition of the Unit of a Penny Weight

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Table of Contents

Introduction
Experimental procedure
Data and observations
Results
Discussion
Conclusion
Works Cited

Introduction

The elusive unit charge of an electron was determined by Robert Millikan’s oil drop experiment in the year 1909, a Nobel laureate. As such, in his experimental setup, and with an aid of X-rays and a pair of charged plates, he was able to suspend an oil droplet on a free fall with the objective of establishing its charge. Basically, a suspended droplet was momentarily subjected to varying X-ray illumination to vital in determine the number of electrons. Consequently, he realized that the quantities of charge were a multiple factor of- 1.6 x 10^-19 C. Conclusively, he established that this was the unit charge of an electron (Millikan 24).

Akin to Millikan’s experiment, the unit weight of a penny can indirectly be determined by simulation. As such, this simulated experiment is designed to determine this parameter indirectly.

Experimental procedure

In this experiment, the students were to be provided with an empty beaker of which they were to be weighed and recorded. The beaker containing all the available pennies and, also the beaker plus half the number of pennies were to be separately weighed and recorded initially before the commencement of the experiment. About 15-20 volunteers- students were to randomly pick a handful of pennies in a beaker (one at a time), weigh and record the observations. Fundamentally, all the pennies were to be returned to the beaker prior to a subsequent handful pick and, counting was prohibited. From the data collected, the smallest difference recorded between handfuls gave the mass of a penny. Consequently, with available data and, with Millikan’s oil drop knowledge of calculation, the weight of a penny was to be obtained.

Data and observations

Sorted data	Difference	Multiples	Average mass per sample (S_ma)
22.59
32.57	9.98	4	2.50
57.50	24.93	10	2.50
72.74	15.24	6	2.54
75.50	2.76	1	2.76
82.53	7.03	3	2.34
85.07	2.54	1	2.54
87.41	2.34	1	2.34
87.64	0.23	0	0.00
92.46	4.82	2	2.41
109.94	17.48	7	2.50
112.13	2.19	1	2.19
120.00	7.87	3	2.62
139.68	19.68	8	2.46
200.21	60.53	25	2.42
215.75	15.54	6	2.59
The average mass of one penny				2.48
Mass of all pennies				1680.36
Number of pennies				~ 678 Pennies

Mass of a penny =2.46 g.
Mass of empty beaker= 170.16 g.
Mass of beaker plus all pennies= 1850.52 g.
Mass of beaker plus a half number of pennies=1010.34 g.

Results

The mass difference is the difference between consecutive masses measured: From the table above, 9.98 is the difference between 32.57 and 22.59. The rest follow suit.

The multiple is obtained as below:

Multiple= (mass difference)/ (mass of a penny).
For instance; 9.98/2.46 ≈4
Average mass per sample = (mass difference)/ (multiple).
For instance; 9.98/4 ≈ 2.50

Therefore, the average mass of one penny (M_avg) is obtained as below:

(∑S_ma)/ (total number S_ma showing significance difference).
= 34.71/14
≈ 2.48g
The total number of pennies= (total mass of pennies)/ M_avg
= (1850.52-170.16)/ 2.48
≈ 678 pennies

Discussion

The main objective of this experiment was to partly establish the weight of a penny indirectly and, partly to simulate how Millikan determined the charge of an electron and what his findings were.

From the simulation, it was established that the average weight of a single penny was approximately 2.5 grams almost tallying with the measured value (2.46 gms.). Analogous to Millikan’s experiment, the handfuls represented the oil droplets while the mass of a single penny represented an electron charge. As such, the random masses represented a varying X-ray illumination hence, on dividing by the mass of a single penny; one is finding the multiples of electron charge.

In his experimental setup, and with an aid of X-rays and a pair of charged plates, Millikan was able to suspend an oil drop on a free fall. With varying X-ray intensity, he was able to vary the charge quantities which were a multiple of 1.6 x10^-19 C- a unit charge of an electron (Millikan 24).

Conclusion

Conclusively, the objective of the experiment was met since it was established that the average mass of a penny was 2.5 grams almost similar to the measured value (2.46 gms.).

Works Cited

Millikan, Robert. The electron and the light-quant from the experimental point of view (Speech). Denver: MacMurray, 1924. Print.

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