A proton has a size of 0.000000000123 and an electron has a size of 1.4x10^-8. How many times smaller is an electron than a proton?
Show your work.
proton = 1.23*10^-11
elec = 1.4*10^-8
elec/prot = 1.4/1.23 * 10^3 = 1138
I thought the proton would have to be in the numerator and the electron would be in the denominator for you to divide?
they ask the ratio of electron to proton. That is, how many times as big is the electron?
The proton is 1/1138 as big as the electron, meaning it is 1138 times as small.
To find out how many times smaller an electron is compared to a proton, we can divide the size of the proton by the size of the electron.
Given:
Size of proton = 0.000000000123
Size of electron = 1.4x10^-8
Dividing the size of the proton by the size of the electron:
(0.000000000123) / (1.4x10^-8)
To divide by a number expressed in scientific notation, we can multiply both the numerator and denominator by the same power of 10 to eliminate the exponent.
(0.000000000123) / (1.4x10^-8) * (10^8 / 10^8)
Simplifying:
0.000000000123 * 10^8 / 1.4
We can use a calculator to evaluate this expression:
0.000000000123 * 10^8 = 123
123 / 1.4 = 87.8571428571
Therefore, the electron is approximately 87.86 times smaller than the proton.