Nuclear Reactions:
Please answer numbers 4,5,6.

4. ¹₁H + ¹³₆C —> ¹⁴₇N + γ

5. ¹₀n + ¹⁰₅B —> ⁷₃Li + ⁴₂He

6. ⁴₂He + ¹⁴₇N —> ¹⁷₈O + ¹₁H

Explanation:

4. ¹₁H + ¹³₆C —> ¹⁴₇N + __

Let ᵇₐX be the unknown.

Thus, the equation becomes:

¹₁H + ¹³₆C —> ¹⁴₇N + ᵇₐX

Next, we shall determine b, a and X. This is illustrated below:

For b:

1 + 13 = 14 + b

14 = 14 + b

Collect like terms

b = 14 – 14

b = 0

For a:

1 + 6 = 7 + a

7 = 7 + a

Collect like terms

a = 7 – 7

a = 0

Therefore,

ᵇₐX => ⁰₀X => γ

Thus, the balanced equation is

¹₁H + ¹³₆C —> ¹⁴₇N + γ

5. ¹₀n + ¹⁰₅B —> __ + ⁴₂He

Let ˣᵧA be the unknown.

Thus, the equation becomes:

¹₀n + ¹⁰₅B —> ˣᵧA + ⁴₂He

Next, we shall determine x, y and A. This can be obtained as follow:

For x:

1 + 10 = x + 4

11 = x + 4

Collect like terms

x = 11 – 4

x = 7

For y:

0 + 5 = y + 2

5 = y + 2

Collect like terms

y = 5 – 2

y = 3

Therefore,

ˣᵧA =>⁷₃A => ⁷₃Li

Thus, the balanced equation is:

¹₀n + ¹⁰₅B —> ⁷₃Li + ⁴₂He

6. ⁴₂He + ¹⁴₇N —> __ + ¹₁H

Let ᶜₑG be the unknown.

Thus, the equation becomes:

⁴₂He + ¹⁴₇N —> ᶜₑG + ¹₁H

Next, we shall determine c, e and G. This can be obtained as follow:

For c:

4 + 14 = c + 1

18 = c + 1

Collect like terms

c = 18 – 1

c = 17

For e:

2 + 7 = e + 1

9 = e + 1

Collect like terms

e = 9 – 1

e = 8

Therefore,

ᶜₑG => ¹⁷₈G => ¹⁷₈O

Thus, the balanced equation is:

⁴₂He + ¹⁴₇N —> ¹⁷₈O + ¹₁H

true tan speed = ang vel x radius