homework set #4; please print and show all work and answers on a separate paper. use correct number of…

homework set #4; please print and show all work and answers on a separate paper. use correct number of significant figures! points will be removed for incorrect number of sig. fig’s 1) roughly speaking, the radius of an atom is about 10,000 times greater than that of its nucleus. if an atom were magnified so that the radius of the nucleus became 2.0 cm, about the size of a marble, what would be the radius of the atom in miles? (1 mi = 1609 m). 2) what is the mass number of an iron atom that has 28 neutrons? 3) for each of the following species, determine the number of protons and the number of neutrons in the nucleus: a. $^{4}_{2}he$ b. $^{25}_{12}mg$ c. $^{48}_{22}ti$ d. $^{79}_{35}br$ 4) write the appropriate symbol for each of the following isotopes (as they would be displayed on a chemical table): a. z=74, a=186

homework set #4; please print and show all work and answers on a separate paper. use correct number of significant figures! points will be removed for incorrect number of sig. fig’s 1) roughly speaking, the radius of an atom is about 10,000 times greater than that of its nucleus. if an atom were magnified so that the radius of the nucleus became 2.0 cm, about the size of a marble, what would be the radius of the atom in miles? (1 mi = 1609 m). 2) what is the mass number of an iron atom that has 28 neutrons? 3) for each of the following species, determine the number of protons and the number of neutrons in the nucleus: a. $^{4}_{2}he$ b. $^{25}_{12}mg$ c. $^{48}_{22}ti$ d. $^{79}_{35}br$ 4) write the appropriate symbol for each of the following isotopes (as they would be displayed on a chemical table): a. z=74, a=186

Answer

Explanation:

Step1: Find the radius of the magnified atom in cm

Given the radius of the nucleus after magnification is $r_{n}=2.0$ cm and the radius of an atom is about 10,000 times greater than that of its nucleus. So the radius of the atom in cm, $r_{a}=10000\times r_{n}$. $r_{a}=10000\times2.0$ cm$ = 20000$ cm

Step2: Convert cm to m

Since 1 m = 100 cm, to convert the radius from cm to m, we use the conversion factor. Let $r_{m}$ be the radius in m. $r_{m}=\frac{20000}{100}$ m$=200$ m

Step3: Convert m to miles

Given 1 mi = 1609 m, let $r_{mi}$ be the radius in miles. $r_{mi}=\frac{200}{1609}$ mi$\approx0.12$ mi

  1. The atomic number of iron (Fe) is $Z = 26$. The mass - number $A$ is the sum of the number of protons and neutrons. Given the number of neutrons $n = 28$. $A=Z + n=26 + 28=54$

a. For $^{4}_{2}He$:

  • The number of protons $Z$ is the sub - script, so $Z = 2$.
  • The number of neutrons $n=A - Z$, where $A = 4$ (the superscript). So $n=4 - 2=2$. b. For $^{25}_{12}Mg$:
  • The number of protons $Z = 12$.
  • The number of neutrons $n=A - Z=25 - 12 = 13$. c. For $^{48}_{22}Ti$:
  • The number of protons $Z = 22$.
  • The number of neutrons $n=A - Z=48 - 22=26$. d. For $^{79}_{35}Br$:
  • The number of protons $Z = 35$.
  • The number of neutrons $n=A - Z=79 - 35 = 44$.
  1. The symbol for an isotope is written as $^{A}{Z}X$, where $Z$ is the atomic number, $A$ is the mass number and $X$ is the chemical symbol. a. Given $Z = 74$ (tungsten, W) and $A = 186$, the symbol is $^{186}{74}W$.

Answer:

  1. $0.12$ mi
  2. 54
  3. a. Protons: 2, Neutrons: 2 b. Protons: 12, Neutrons: 13 c. Protons: 22, Neutrons: 26 d. Protons: 35, Neutrons: 44
  4. a. $^{186}_{74}W$