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

Step-by-step 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

Answer:

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

Step-by-step explanation:

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

$\implies \sf \dfrac{mass\:of\:neutron}{mass \: of \: electron}=\dfrac{2 \times 10^{-24}}{9 \times 10^{-28}}$

Rewrite:

$\implies \sf \dfrac{2}{9} \times \dfrac{10^{-24}}{10^{-28}}$

$\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies \sf \dfrac{2}{9} \times 10^{-24-(-28)}$

Simplify:

$\implies \sf \dfrac{2}{9} \times 10^{4}$

$\implies \sf 0.\.{2} \times 10^{4} \approx 2000$

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

Check

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