What is the energy change ∆E (in kJ/mol) when an a particle is emitted from 174Ir? The atomic mass of 174Ir is 173.96666 the atomic mass of 170Re is 169.95804, and the atomic mass of a 4He atom is 4.00260.

Video transcript

Welcome back everyone. We need to determine the energy change delta and killed jules per mole. When strontium 83 emits an alpha particle. We're going to use the term for C being our speed of light equal to 99 792458 m per second. And the following atomic masses. For strontium 83 Krypton 79 helium four. And were given the reaction for the decay of strong team 83 which forms krypton 79 helium four as products which really is representative of our alpha particle. So in order to determine our energy change delta E. We first need to figure out our mass defect. Delta M. Recall that this is found by taking the sum of the mass of our reactant. Subtracted from the sum of our mass of our products. And so in terms of our equation, we would say that our mass defect is equal to our mass of our strontium 83 reactant In total subtracted from the sum between our massive products being our massive Krypton 79 plus our mass of our alpha particle. And sorry, this is a parentheses. So plugging in our given masses from the prompt, we can say that our mass effect is equal to our massive strontium which is given in the prompt as 82.91756. Recall that the units are going to be in atomic mass units. This is subtracted from our mass of krypton given the prompt as 78.920083 am. Use added to our mass of our second product which is our alpha particle which has a mass given in the prompt As 4.00-60 a. m. use. And so this should actually be parentheses within brackets here And so we will be able to simplify and figure out that are massed effect is equal to the difference between 82.91756. And I'm sorry this is amused subtracted from the result of our brackets being 82.92- AM use. And sorry just for more accuracy will say that it's 82.922683 AM use for the result of our brackets and taking the difference we find that our mass defect is equal to a value of five, sorry, negative 5.123 times 10 to the negative third power a muse. Now note that this is a negative value. And so therefore we would say that energy is absorbed by our system which is our reaction. Next. We want to continue and use this mass defect to find our energy change delta T. By recalling that we can use the following formula where delta E. Is equal to our mass defect times the speed of light squared. Now we should recognize that we have a conversion factor where one atomic mass unit is equivalent to one g Permal. And so that is how we would interpret our mass defect in order to get to our energy change in the proper units which we should recall will be in units of killing joules per mole. So let's begin by plugging in what we know we're solving for delta E. We know our mass defect which we just found above as negative 5.1 times 10 to the negative third power. We're no longer using units of AM US because we understand that one a.m. U. Is equivalent to one g per mole. So that is the unit that we're using. And then we will incorporate our speed of light which we're told to use in the prompt as the value to 99 m per second which is squared. And because we notice that we have killed jules as our unit for our energy change. We're actually going to want to convert our mass effect from grams per mole, two kg per mole. And so we would have grams in the denominator and kilograms in the numerator in which we would recall that our prefix kilo tells us that we have an equivalent of 10 to the negative third power kilograms to one g. And so canceling out grams were left with kilograms times meters per second squared, divided by moles as our final units and simplifying everything by taking the product of our right hand side. We would find that our mass defect is equal to a value of negative 4.60 times 10 to the 11th power. And our units we have our again, as we stated, kilograms times meters squared Divided by 2nd squared times most in which now we want to recall our conversion factor where one jewel is equivalent to one kg times meter squared divided by seconds squared. And we can also recall that one jewel is equivalent to one times 10 to the negative third power killed jules. And so converting our units of energy change delta T. We would begin with what we calculated above negative 4.60 times 10 to the 11th Power, kilograms times meters squared divided by seconds squared times second squared, sorry, times most. We want to get to jewels in our numerator first. So we're going to multiply by the conversion factor where we understand that one kg times meter squared divided by seconds squared, has an equivalent to one Juul. And so this allows us to cancel out kilograms times meters squared in the numerator as well as second squared here with the denominator. And now we're at jewels and we need again, our final units of energy change to be in kilograms per mole. And so we have to convert from jewels to kill a jules. So recalling that one jewel has an equivalent of one times 10 to the negative third power. Kill jules. We can now cancel out jewels and our final units are now killing joules per mole, which is what we want for our energy change. And so we would get a final result of negative 4.60 times 10 to the 11th power kila jules. Permal Sorry correction. We have a different power of 10 because we're multiplying by 10 to the negative third power Which is over here. And so our final result is actually equal to negative 4.60 times 10 to the positive eighth power. In units of kila jules per mole. And so what's highlighted In yellow represents our final answer as our energy change in kg per mole. When strontium 83 emits an alpha particle and this will correspond to choice a in the multiple choice as our final answer. So I hope this was helpful. And let us know if you have any questions