Balance the following nuclear equations by filling in the blanks. (a) Es-249 + neutron \(\longrightarrow 2\) neutrons \(+\) ____\(+\) Gd-161 (b) ______ \(\longrightarrow\) beta particle \(+\mathrm{Co}-59\) (c) \(4 \mathrm{HH} \longrightarrow\)______ \(+2\) positrons (d) \(\mathrm{Mg}-24+\) neutron \(\longrightarrow\) proton \(+\) ________

: First, we should identify the initial number of protons and neutrons in this reaction. Es-249 has 99 protons and 150 neutrons, and there is also 1 extra neutron. The number of protons and neutrons after the reaction can be found by considering both the neutrons and Gd-161. Gd-161 has 64 protons and 97 neutrons, and there are 2 neutrons produced. Now, we need to find the missing element, which should have the same total number of protons and neutrons as Es-249 and the neutron. Using the conservation of protons and neutrons, we have: Initial total protons: \(99\) Initial total neutrons: \(150+1=151\) Final total protons: \(64 + X\) Final total neutrons: \(97+2=99\) Protons: \(99 = 64+X\), \(X=35\) Neutrons: \(151 = 99 + Y\), \(Y=52\) So, the missing element has 35 protons and 52 neutrons, which is Br-87. The balanced equation is: \(Es-249 + n \rightarrow 2n + Br-87 + Gd-161\)

: Since a beta particle is an electron, its production in a nuclear reaction increases the number of protons in the final product by 1. We can find the missing element by adding 1 proton to Co-59, which has 27 protons and 32 neutrons. The missing element has 28 protons and 32 neutrons, which is Ni-60. The balanced equation is: \(Ni-60 \rightarrow \beta^- + Co-59\)

: In this reaction, we have 4 hydrogen nuclei - each with 1 proton and no neutrons. Let's find the number of protons and neutrons in the final element and write the balanced equation. Initial total protons: \(4 * 1 = 4\) Initial total neutrons: \(4*0=0\) Final total protons: \(X - 2\) Final total neutrons: \(Y\) Protons: \(4 = X - 2\), \(X=6\) Neutrons: \(Y=0\) The resulting element is C-6. The balanced equation is: \(4HH \rightarrow C-6 + 2e^{+}\)

: First, identify the number of protons and neutrons before and after the reaction. Mg-24 has 12 protons and 12 neutrons. Adding a neutron, we have: Initial total protons: \(12\) Initial total neutrons: \(12+1=13\) To balance the nuclear equation, we subtract a proton from the initial total: Final total protons: \(12 -1 = 11\) The final product must have 11 protons and 13 neutrons, which is Na-24. The balanced equation is: \(\mathrm{Mg}-24 + n \rightarrow p + Na-24\)