Question

show work for the following problems!!!

1. the mass and percent abundance for the isotopes of three unknown elements are given below

a. find the mass of each individual isotope shown in each diagram.
b. then find the mass of the unknown elements using weighted averages.
c. element “x”
three circles with neutron, proton counts and percentages: first 8 n⁰, 8 p⁺, 99.959 %; second 9 n⁰, 8 p⁺, 0.037 %; third 10 n⁰, 8 p⁺, 0.204%
d. element “y”
two circles: first 18 n⁰, 17 p⁺, 75.77%; second 20 n⁰, 17 p⁺, 24.23%
e. element “z”
four circles: first 16 n⁰, 16 p⁺, 95.002%; second 17 n⁰, 16 p⁺, 0.76%; third 18 n⁰, 16 p⁺, 4.22%; fourth 20 n⁰, 16 p⁺, 0.014%

1. zinc has 5 different isotopes. each isotope and the percent abundance is given in the following table. what is the mass of zinc that should be listed on the periodic table?

% abundance	48.89%	27.81%	4.110 %	18.57 %	0.6200%
isotope	zn - 64	zn - 66	zn - 67	zn - 68	zn - 70

Explanation:

Step1: Calculate isotope mass (X)

Isotope mass = protons + neutrons

1. $8p^+ +8n^o = 16$
2. $8p^+ +9n^o = 17$
3. $8p^+ +10n^o = 18$

Step2: Weighted avg for Element X

Multiply mass by % (decimal), sum.
$$(16 \times 0.9959) + (17 \times 0.0037) + (18 \times 0.00204)$$
$$=15.9344 + 0.0629 + 0.03672 = 16.03402$$

Step3: Calculate isotope mass (Y)

1. $17p^+ +18n^o = 35$
2. $17p^+ +20n^o = 37$

Step4: Weighted avg for Element Y

$$(35 \times 0.7577) + (37 \times 0.2423)$$
$$=26.5195 + 8.9651 = 35.4846$$

Step5: Calculate isotope mass (Z)

1. $16p^+ +16n^o = 32$
2. $16p^+ +17n^o = 33$
3. $16p^+ +18n^o = 34$
4. $16p^+ +20n^o = 36$

Step6: Weighted avg for Element Z

$$(32 \times 0.95002) + (33 \times 0.0076) + (34 \times 0.0422) + (36 \times 0.00014)$$
$$=30.40064 + 0.2508 + 1.4348 + 0.00504 = 32.09128$$

Step7: Weighted avg for Zinc

Multiply isotope mass by % (decimal), sum.
$$(64 \times 0.4889) + (66 \times 0.2781) + (67 \times 0.04110) + (68 \times 0.1857) + (70 \times 0.006200)$$
$$=31.2896 + 18.3546 + 2.7537 + 12.6276 + 0.434 = 65.4595$$

Answer:

1. Element X isotope masses: 16, 17, 18; Average atomic mass: $\approx 16.03$
2. Element Y isotope masses: 35, 37; Average atomic mass: $\approx 35.48$
3. Element Z isotope masses: 32, 33, 34, 36; Average atomic mass: $\approx 32.09$
4. Zinc average atomic mass (periodic table value): $\approx 65.46$