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Calculate the atomic mass of the unknown element X described below Isotope & Percent Abundance 204_(X) & 1.37 206_(X) & 26.26 207_(X) & 20.82 208_(X) & 51.55 (A) 204 mathrm(amu) (B) 206 mathrm(amu) (C) 207 mathrm(amu) (D) 208 mathrm(amu)

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Calculate the atomic mass of the unknown element X described below

 Isotope & Percent Abundance 
 204_(X) & 1.37 
 206_(X) & 26.26 
 207_(X) & 20.82 
 208_(X) & 51.55 


(A) 204 mathrm(amu) 
(B) 206 mathrm(amu) 
(C) 207 mathrm(amu) 
(D) 208 mathrm(amu)

Calculate the atomic mass of the unknown element X described below Isotope & Percent Abundance 204_(X) & 1.37 206_(X) & 26.26 207_(X) & 20.82 208_(X) & 51.55 (A) 204 mathrm(amu) (B) 206 mathrm(amu) (C) 207 mathrm(amu) (D) 208 mathrm(amu)

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SaffronProfessional · Tutor for 6 years

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#Explanation<br />The atomic mass of an element is calculated by taking the sum of the products of the mass of each isotope and its relative abundance. In this case, we have four isotopes of the element X, each with a different mass and relative abundance. <br /><br />The relative abundance is given as a percentage, so we need to convert these percentages to a decimal form by dividing each by 100. <br /><br />The atomic mass (AM) can be calculated using the following formula:<br /><br />\( AM = \sum (mass_{isotope} \times abundance_{isotope}) \)<br /><br />Substituting the given values into the formula, we get:<br /><br />\( AM = (204 \times 0.0137) + (206 \times 0.2626) + (207 \times 0.2082) + (208 \times 0.5155) \)<br /><br />#Answer<br />Performing the calculations, we find:<br /><br />\( AM = 2.7948 + 54.1352 + 43.0964 + 107.184 \)<br /><br />Adding these together gives:<br /><br />\( AM = 207.2104 \)<br /><br />Therefore, the atomic mass of the element X is closest to 207 amu. So, the correct answer is (C) \( 207 \mathrm{amu} \).
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