Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each (Al-27 = 26.981538 amu, Am-241 = 241.056822 amu, He-4 = 4.002603 amu, Np-237 = 237.048166 amu, P-30 = 29.981801 amu, S-32 = 31.972071 amu, and Si-29 = 28.976495 amu).
a. ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ____

Question

Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each (Al-27 = 26.981538 amu, Am-241 = 241.056822 amu, He-4 = 4.002603 amu, Np-237 = 237.048166 amu, P-30 = 29.981801 amu, S-32 = 31.972071 amu, and Si-29 = 28.976495 amu).
a. ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ____

a. ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ____

Accepted Answer

Welcome back, everyone find the missing species in the following nuclear equation and calculate the energy change per mole of Argan 34. In order to identify the missing species, we have to use the law of mass conservation and charge conservation. So if we look at our masses on the left hand side, we have 34. Let's assume that the missing species has a form of X with a mass of M and an atomic number of C. So essentially, if we take our mass number of 34 and if we add the mass number of X, which is M, this should be equal to the total mass of the products. So 31 plus four, if we simplify the equation for this expression, we get 34 plus M equals 35. And therefore the mass number of the unknown must be one. Number two, we want to identify the atomic number using the law of charge conservation. So now we're taking the bottom numbers, we're taking 18 from Oregon. And if we add C from X, we must get a sum which is equal to 16 plus two. On the product side, simplifying, we get 18 plus C equals 18, which essentially tells that the atomic number C where the charge is equal to zero. So our species X simply has a mass number of one and the atomic number of zero, which is essentially a neutron, a mass of one and a charge of zero, right. So we can essentially replace X with N which represents a neutron. We have successfully found the missing species. And our next step is to identify the energy change per mole of organ. So let's label it as our third step. And we want to recall that the energy change is calculated using the mass defect formula. Specifically, we want to identify the mass defect delta M which is the sum of the masses of reactants minus the sum of the masses of products. Now, let's begin with the masses of reactants. And our first reactant is Argon 34 with the atomic mass of 33.9802 atomic mass units. And we want to add the mass of one neutron. It has an atomic mass of 1.0086 atomic mass units. And we want to subtract the masses of products starting with sulfur 31 that would be 30.9795. And we're also going to subtract the mass of helium. That'd be 4.0026 atomic mass units. We obtain a number which is equal to 0.0067 atomic mass units. Now, if we want to get the energy change, we have to move on to step number four and use the equation delta E equals delta mc squared. So our mass defect delta M is 0.0067 atomic mass units. But we want to use kilograms, right? Because the the si unit of mass is a kilogram. So we're going to introduce dimensional analysis relating one atomic mass unit to its expression in kilograms. That'd be 1.66054 multiplied by sense, the power of negative 27 kg, this gives us the mass defect in kilograms. And now we want to multiply the answer by the speed of light squared, which is 3.00 multiplied by 10 to the eighth meters per second squared. Now, it is really important to understand that there is one more part that is missing. We have calculated the energy change per nucleus of organ, but we are asked to calculate it to calculate that result per mole. And since one mole has avo gator's number of nuclei, we're going to multiply our result by aviator's number, which will give us our answer per mole of organ rather than one nucleus. And therefore, if we calculate the result, we get our final answer of 6.0 multiplied by sense, the power of 11th jules per month, that would be our final answer. We have identified the missing species. That's a neutron, right? And the energy change promo of organ 34. Thank you for watching.

Verified Solution

Key Concepts

Nuclear Reactions

Mass-Energy Equivalence

Atomic Mass Units (amu)