Balance the following nuclear equations by filling in the...

Balance the following nuclear equations by filling in the blanks: (a) Es- $240+$ neutron $\longrightarrow 2$ neutrons+______+ Gd-161 (b)______ $\longrightarrow \beta$ -particle $+$ Co-59 (c) $4_{1}^{1} \mathrm{H} \longrightarrow \underline{ }+2$ positrons (d)_____ $\mathrm{Mg}-24+$ neutron $\longrightarrow$ proton $+$______

Balance the following nuclear equations by filling in the blanks:
(a) Es- $240+$ neutron $\longrightarrow 2$ neutrons+______+ Gd-161
(b)______ $\longrightarrow \beta$ -particle $+$ Co-59 (c) $4_{1}^{1} \mathrm{H} \longrightarrow \underline{ }+2$ positrons
(d)_____ $\mathrm{Mg}-24+$ neutron $\longrightarrow$ proton $+$______

Key Concepts

Conservation Laws in Nuclear Reactions

In any nuclear reaction, both the mass number (total number of protons and neutrons) and the atomic number (number of protons) must be conserved. This fundamental principle guides the balancing process by ensuring that all nucleons and overall charge remain accounted for before and after the reaction.

Nuclear Reaction Mechanisms

Nuclear reactions can include various processes such as neutron capture, particle emission, and radioactive decay. Understanding which particles are involved and how they transform or are exchanged is crucial for setting up and balancing the overall nuclear equation correctly.

Beta Decay

Beta decay is a process where a neutron transforms into a proton (or vice versa in beta-plus decay), accompanied by the emission of a beta particle (electron in beta-minus decay or positron in beta-plus decay) and a neutrino. This decay alters the atomic number while keeping the mass number constant, which is essential when balancing equations involving beta emissions.

Positron Emission

Positron emission (a form of beta-plus decay) involves the conversion of a proton into a neutron, releasing a positron and a neutrino. This type of decay decreases the atomic number without affecting the mass number, and recognizing it is important for correctly balancing equations that feature positron production.

Transcript

00:01 So for this question we have the following nuclear equations and they want us to fill in the blank so for part a in order to determine what the blank is all we need to know is that the sum of the atomic number on both sides must be equal to each other and the sum of the atomic mass on both sides must be equal to each other so for part a we can first determine the atomic number of es and gd by looking at the pr table and we see that is 99 for es and that is 64 for gd now we have 99 on the left side plus the 0 from the neutron.

00:34 On the right side, we have 0 from the neutron plus 64 from gd.

00:41 In order to balance it out, we need to add 35.

00:45 If we put 35 here and when we look at the pr we'll look at the pr, now asphidi mass, we have 240 on the left plus d1 from the neutron.

00:53 Now on the right, we have one from the neutron, but since we have two of them, we need to multiply it by 2, plus the 161 from gd in order to find out what's missing.

01:02 All we need to know is subtract the sum on the left from the numbers on the right.

01:08 And we should get 78.

01:10 So we add 78 to the right side.

01:15 Now for part b, we have negative 1 on the right.

01:21 Now for co for coppo, the atomic number is 27.

01:25 So it plus 27, that is 26, right? so we put 26 here and we know that that is iron.

01:31 As for the mass, we have 0 on the right from the electron plus 59 from co, so that is equal to 59.

01:39 We put 59 here...