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
- [tex]2 x10^{-24} / (9 x10^{-28} )[/tex]
= [tex](2/9) x10^{-24--28}[/tex]
= [tex](2/9)x10^{-24+28}[/tex]
≈ [tex]0.2222x10^{28-24}[/tex]
≈ [tex]0.2222x10^{4}[/tex]
≈ 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:
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:
[tex]\implies \sf \dfrac{mass\:of\:neutron}{mass \: of \: electron}=\dfrac{2 \times 10^{-24}}{9 \times 10^{-28}}[/tex]
Rewrite:
[tex]\implies \sf \dfrac{2}{9} \times \dfrac{10^{-24}}{10^{-28}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \sf \dfrac{2}{9} \times 10^{-24-(-28)}[/tex]
Simplify:
[tex]\implies \sf \dfrac{2}{9} \times 10^{4}[/tex]
[tex]\implies \sf 0.\.{2} \times 10^{4} \approx 2000[/tex]
Therefore, the mass of a neutron is approximately 2,000 times the mass of an electron.
Check
[tex]\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}[/tex]
