Question

The mass of an electron is approximately 9 × 10-28 grams, while the mass of a neutron is approximately 2 × 10-24 grams. Which of the following is true?

A. The mass of a neutron is approximately 10,000 times the mass of an electron.
B. The mass of a neutron is approximately 1,000 times the mass of an electron.
C. The mass of a neutron is approximately 2,000 times the mass of an electron.
D. The mass of a neutron is approximately 20,000 times the mass of an electron.

Answer 1

Answer: the mass of a neutron is approximately 2,000 times the mass of an electron

Explanation:

- the easiest way to solve this (in my opinion) is to simply divide the mass of a neutron by the mass of an electron

-
`2 x10^(-24) / (9 x10^(-28) )`

=
`(2/9) x10^(-24--28)`

=
`(2/9)x10^(-24+28)`

≈
`0.2222x10^(28-24)`

≈
`0.2222x10^(4)`

≈ which is approximately 2222

- so 2222 is approximately 2000 times

- therefore, the mass of a neutron is approximately 2,000 times the mass of an electron

hope this helps :)

Answer 2

C. The mass of a neutron is approximately 2,000 times the mass of an electron.

Explanation:

Divide the mass of the neutron by the mass of the electron:

`\implies \sf (mass\:of\:neutron)/(mass \: of \: electron)=(2 * 10^(-24))/(9 * 10^(-28))`

Rewrite:

`\implies \sf (2)/(9) * (10^(-24))/(10^(-28))`

`\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`\implies \sf (2)/(9) * 10^(-24-(-28))`

Simplify:

`\implies \sf (2)/(9) * 10^(4)`

`\implies \sf 0.\.{2} * 10^(4) \approx 2000`

Therefore, the mass of a neutron is approximately 2,000 times the mass of an electron.

Check

`\begin{aligned}\textsf{mass of neutron} & = \sf \textsf{mass of electron} * 2000\\\implies \textsf{mass of neutron} & =\sf 9 * 10^(-28)* 2000\\& =\sf 9 * 10^(-28)* 2 * 10^3\\& =\sf 18 * 10^(-28+3)\\& =\sf 18 * 10^(-25)\\& = \sf 1.8 * 10^(-24)\\& \approx \sf 2 * 10^(-24)\end{aligned}`