Question 41 of 62intermediate🔧 ApplyNumerical2 marks

An element with mass number 81 contains 31.7% more neutrons as compared to protons. Assign the atomic symbol.

Correct Answer

The atomic symbol of the element is 3581Br^{81}_{35}\text{Br}.

Exercise: EXERCISES | Q: 2.42 | (Page 41)
For More Understanding

Explanation

The mass number (A) is the sum of protons (Z) and neutrons (n). By setting up an equation using the given percentage increase in neutrons relative to protons, we can solve for the atomic number (Z). Rounding to the nearest whole number gives Z = 35, which corresponds to the element Bromine (Br) as seen in the provided examples.

Solution Steps

  1. Step 1: Let the number of protons be ZZ and the number of neutrons be nn. The mass number A=81A = 81.

  2. Step 2: The element contains 31.7% more neutrons than protons. Therefore, n=Z+0.317Z=1.317Zn = Z + 0.317Z = 1.317Z.

  3. Step 3: Using the formula for mass number, A=Z+nA = Z + n, we substitute the values: 81=Z+1.317Z=2.317Z81 = Z + 1.317Z = 2.317Z.

  4. Step 4: Solving for ZZ, we get Z=812.317≈34.95Z = \frac{81}{2.317} \approx 34.95. Since the number of protons must be a whole number, Z=35Z = 35.

  5. Step 5: The number of neutrons is n=81−35=46n = 81 - 35 = 46.

  6. Step 6: The atomic number 35 corresponds to the element Bromine (Br). Thus, the atomic symbol is 3581Br^{81}_{35}\text{Br}.

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