The relative atomic mass (A_r) of atoms is the average mass of all the different isotopes of an element (taking into account the amount of each isotopes) on a scale weere ^12C atoms have mass of exactly 12.

Question

Element Krypton isotopes 78 36 Kr 80 36 Kr 82 36 Kr 84 36 Kr Abundance 0.4% 2.3% 11.6% 11.5 % 57.0% Relative atomic mass (A_r) to (3sf) ___

Answer 1

To calculate the relative atomic mass (A_r) of Krypton based on the given isotopes and their abundances, follow these steps:

1. List the isotopes and their masses:

   • \(^{78}\text{Kr}\) = 78
   • \(^{80}\text{Kr}\) = 80
   • \(^{82}\text{Kr}\) = 82
   • \(^{84}\text{Kr}\) = 84

2. List the abundances:

   • \(^{78}\text{Kr}\): 0.4% = 0.004
   • \(^{80}\text{Kr}\): 2.3% = 0.023
   • \(^{82}\text{Kr}\): 11.6% = 0.116
   • \(^{84}\text{Kr}\): 11.5% = 0.115
   • \(^{86}\text{Kr}\): 57.0% = 0.570 (corrected to include)

3. Calculate the contribution of each isotope to the relative atomic mass:

   • \( \text{Contribution from } ^{78}\text{Kr} = 78 \times 0.004 = 0.312 \)
   • \( \text{Contribution from } ^{80}\text{Kr} = 80 \times 0.023 = 1.84 \)
   • \( \text{Contribution from } ^{82}\text{Kr} = 82 \times 0.116 = 9.512 \)
   • \( \text{Contribution from } ^{84}\text{Kr} = 84 \times 0.115 = 9.66 \)

4. Calculate the total A_r:

   • \( A_r = 0.312 + 1.84 + 9.512 + 9.66 + (mass of additional isotope and it's contribution)\)

Noting that the total mass contribution from each isotope is calculated collectively, now let’s do the summary iteration:

\[ A_r = 0.312 + 1.84 + 9.512 + 9.66 + (contribution for , ^{86}\text{Kr} = 86 \times 0.570) \]

Calculate: \[ A_r = 0.312 + 1.84 + 9.512 + 9.66 + 48.82 \] \[ A_r = 0.312 + 1.84 + 9.512 + 9.66 + 48.82 = 70.142 \text{ rounded to 3sf} = 70.1 \]

Thus the calculated relative atomic mass (A_r) for Krypton to three significant figures is 70.1.