Complete and balance the following nuclear equations by supplying the missing particle: \begin{equation}\begin{array}{l}{\text { (a) }_{17}^{14} \mathrm{N}+_{2}^{4} \mathrm{He} \longrightarrow ? +_{1}^{1} \mathrm{H}} \\ {\text { (b) }_{19}^{40} \mathrm{K}+_{1}^{0} \mathrm{e} \ \mathrm{(orbital \ electron) \longrightarrow ?}}\\\ {\text { (c) }_{}{} \mathrm{?}+_{2}^{4} \mathrm{He} \longrightarrow_{14}^{30} \mathrm{Si} +_{1}^{1} \mathrm{H}}\\\ {\text { (d) }_{26}^{58} \mathrm{Fe} +2 _{0}^{1} \mathrm{n} \longrightarrow_{27}^{60} \mathrm{Co}+?}\\\ {\text { (e) }_{92}^{235} \mathrm{U}\longrightarrow+_{0}^{1} n \longrightarrow_{54}^{135} \mathrm{Xe}+2_{0}^{1} \mathrm{n}+?} \end{array}\end{equation}

Step by step solution

01

Determine the missing particle's atomic and mass numbers

First, we need to find out the atomic number (Z) and mass number (A) of the unknown particle (?). We will use the fact that in a balanced nuclear equation, the total atomic numbers (Z) and mass numbers (A) are conserved.

02

Write down the equation for atomic number conservation

\( Z_1 + Z_2 = Z_3 + Z_4 \Rightarrow 17 + 2 = Z_3 + 1 \) Solving for Z3: \( Z_3 = 18\)

03

Write down the equation for mass number conservation

\( A_1 + A_2 = A_3 + A_4 \Rightarrow 14 + 4 = A_3 + 1 \) Solving for A3: \( A_3 = 17 \) The missing particle is \(_{18}^{17}O\). The balanced equation is: \(_{17}^{14}N\ +\ _{2}^{4}He\ \longrightarrow\ _{18}^{17}O\ +\ _{1}^{1}H\) (b) Balancing the nuclear equation:

04

Determine the missing particle's atomic and mass numbers

Use the conservation laws for atomic number and mass number to identify the unknown particle.

05

Write down the equation for atomic number conservation

\( Z_1 + Z_2 = Z_3 \Rightarrow 19 = Z_3 \)

06

Write down the equation for mass number conservation

\( A_1 + A_2 = A_3 \Rightarrow 40 = A_3 \) The missing particle is \(_{19}^{40}Ca\). The balanced equation is: \(_{19}^{40}K\ +\ _{1}^{0}e\ \longrightarrow\ _{19}^{40}Ca\) (c) Balancing the nuclear equation:

07

Determine the missing particle's atomic and mass numbers

Use the conservation laws for atomic number and mass number to identify the unknown particle.

08

Write down the equation for atomic number conservation

\( Z_1 + Z_2 = Z_3 + Z_4 \Rightarrow Z_1 + 2 = 14 + 1 \) Solving for Z1: \( Z_1 = 13\)

09

Write down the equation for mass number conservation

\( A_1 + A_2 = A_3 + A_4 \Rightarrow A_1 + 4 = 30 + 1 \) Solving for A1: \( A_1 = 27 \) The missing particle is \(_{13}^{27}Al\). The balanced equation is: \(_{13}^{27}Al\ +\ _{2}^{4}He\ \longrightarrow\ _{14}^{30}Si\ +\ _{1}^{1}H\) (d) Balancing the nuclear equation:

10

Determine the missing particle's atomic and mass numbers

Use the conservation laws for atomic number and mass number to identify the unknown particle.

11

Write down the equation for atomic number conservation

\( Z_1 + Z_2 = Z_3 \Rightarrow 26 + 0 = 27\)

12

Write down the equation for mass number conservation

\( A_1 + A_2 = A_3 + A_4 \Rightarrow 58 + 1 = 60 + A_4 \) Solving for A4: \( A_4 = -1 \) The missing particle is \(_{0}^{-1}e^-\). The balanced equation is: \(_{26}^{58}Fe\ +\ _{0}^{1}n\ \longrightarrow\ _{27}^{60}Co\ +\ _{0}^{-1}e^-\) (e) Balancing the nuclear equation:

13

Determine the missing particle's atomic and mass numbers

Use the conservation laws for atomic number and mass number to identify the unknown particle.

14

Write down the equation for atomic number conservation

\( Z_1 + Z_2 = Z_3 + Z_4 + Z_5 \Rightarrow 92 = 54 + 0 + Z_5 \) Solving for Z5: \( Z_5 = 38\)

15

Write down the equation for mass number conservation

\( A_1 + A_2 = A_3 + A_4 + A_5 \Rightarrow 235 + 1 = 135 + 1 + A_5 \) Solving for A5: \( A_5 = 99 \) The missing particle is \(_{38}^{99}Sr\). The balanced equation is: \(_{92}^{235}U\ +\ _{0}^{1}n\ \longrightarrow\ _{54}^{135}Xe\ +\ _{0}^{1}n\ +\ _{38}^{99}Sr\)

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