Question

Using the given charge-to-mass ratios for electrons and protons, and knowing the magnitudes of their charges are equal, what is the ratio of the proton’s mass to the electron’s? (Note that since the charge-to-mass ratios are given to only three-digit accuracy, your answer may differ from the accepted ratio in the fourth digit.)

What is the ratio of the proton’s mass to the electron’s based on the given information?

A. 1836:1
B. 2000:1
C. 2055:1
D. 2200:1

Answer 1

The ratio of the proton's mass to the electron's mass is approximately 1836:1, based on their charge-to-mass ratios and the fact that their charges are equal in magnitude.

Step-by-step explanation:

Using the charge-to-mass ratios for electrons and protons and knowing that the magnitudes of their charges are equal, the ratio of the proton's mass to the electron's mass can be found. Since the proton's charge-to-mass ratio is 1836 times less than the electron's (given that for an electron, the charge-to-mass ratio is higher due to its much smaller mass), this means that the proton's mass is roughly 1836 times that of the electron's mass.

The ratio of the proton's mass to the electron's mass can be determined using the charge-to-mass ratios of the two particles. Since the magnitudes of their charges are equal, we can compare the ratios of their charges to determine the mass ratio. The charge-to-mass ratio for the electron is approximately 1.76 x 10^11 C/kg, while the charge-to-mass ratio for the proton is approximately 9.58 x 10^7 C/kg. Dividing these two ratios gives us:

Proton mass to electron mass ratio = (9.58 x 10^7 C/kg) / (1.76 x 10^11 C/kg)

Simplifying this expression gives us a ratio of approximately 1836:1. Therefore, the correct answer is A. 1836:1.

Therefore, the answer to the question is that the ratio of the proton's mass to the electron's mass is approximately 1836:1, which corresponds to option A.