Physics for Scientists and Engineers with Modern Physics, Technology Update
Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 45, Problem 30P

(a)

To determine

Identify nucleus A.

(a)

Expert Solution
Check Mark

Answer to Problem 30P

The nucleus A is nitrogen and its symbol is 713N.

Explanation of Solution

A highly energized proton is absorbed by the 612C and produces an unknown nucleus A and a gamma ray.

    11H+612C??A+γ

The atomic number of  11H is Z=1 and its mass number is A=1, and the atomic number of 612C is Z=6 and its mass number A=12. Thus, the atomic and mass number for the unknown nucleus A is Z=1+6=7 and A=1+12=13 respectively.

In periodic table, the element with atomic number Z=7 is nitrogen, 713N. The reaction becomes,

    11H+612C713N+γ

Thus, the nucleus A is nitrogen and its symbol is 713N.

(b)

To determine

Identify nucleus B.

(b)

Expert Solution
Check Mark

Answer to Problem 30P

The nucleus B is carbon and its symbol is 613C.

Explanation of Solution

As 713N is the isotope of nitrogen, it decays by emitting a positron and a neutrino.

    713N?+10e+ν

The atomic and mass number for the nitrogen is Z=7 and A=13 respectively. Thus, the atomic and mass number of unknown nucleus B is Z=71=6 and A=130=13.

In periodic table, the element with atomic number Z=6 is carbon, 613C. The reaction becomes,

    713N613C+10e+ν

Thus, the nucleus B is carbon and its symbol is 613C.

(c)

To determine

Identify nucleus C.

(c)

Expert Solution
Check Mark

Answer to Problem 30P

The nucleus C is nitrogen and its symbol is 714N.

Explanation of Solution

613C nucleus absorbs a proton and produce nucleus C along with the emission of gamma ray.

    11H+613C?+γ

The atomic number of  11H is Z=1 and its mass number is A=1, and the atomic number of 613C is Z=6 and its mass number A=13. Thus, the atomic and mass number for the unknown nucleus A is Z=1+6=7 and A=1+13=14 respectively.

In periodic table, the element with atomic number Z=7 is nitrogen, 714N. The reaction becomes,

    11H+613C714N+γ

Thus, the nucleus C is nitrogen and its symbol is 714N.

(d)

To determine

Identify nucleus D .

(d)

Expert Solution
Check Mark

Answer to Problem 30P

The nucleus D is oxygen and its symbol is 815O.

Explanation of Solution

A proton is absorbed by the 714N and produces an unknown nucleus D and a gamma ray.

    11H+714N?+γ

The atomic number of  11H is Z=1 and its mass number is A=1, and the atomic and mass number for the nitrogen is Z=7 and A=14 respectively. Thus, the atomic and mass number of unknown nucleus D is Z=7+1=8 and A=14+1=15.

In periodic table, the element with atomic number Z=8 is oxygen, 815O. The reaction becomes,

    11H+714N815O+γ

Thus, the nucleus D is oxygen and its symbol is 815O.

(e)

To determine

Identify nucleus E.

(e)

Expert Solution
Check Mark

Answer to Problem 30P

The nucleus E is nitrogen and its symbol is 715N.

Explanation of Solution

As 815O is the isotope of oxygen, it decays by emitting a positron and a neutrino.

    815O?+10e+ν

The atomic and mass number for the nitrogen is Z=8 and A=18 respectively. Thus, the atomic and mass number of unknown nucleus B is Z=81=7 and A=150=15.

In periodic table, the element with atomic number Z=7 is nitrogen, 715N. The reaction becomes,

    815O715N+10e+ν

Thus, the nucleus E is nitrogen and its symbol is 715N.

(f)

To determine

Identify nucleus F.

(f)

Expert Solution
Check Mark

Answer to Problem 30P

The nucleus F is carbon and its symbol is 612C.

Explanation of Solution

A 715N nucleus absorbs a proton and produces an unknown nucleus F and alpha particle.

    11H+715N?+24He

The atomic number of  11H is Z=1 and its mass number is A=1, and the atomic and mass number for the nitrogen is Z=7 and A=15 respectively. Thus, the atomic and mass number of unknown nucleus F is Z=7+12=6 and A=15+14=12.

In periodic table, the element with atomic number Z=6 is carbon, 612C. The reaction becomes,

    11H+715N612C+24He

Thus, the nucleus F is carbon and its symbol is 612C.

(g)

To determine

The significance of the final nucleus in the last step of the carbon cycle.

(g)

Expert Solution
Check Mark

Answer to Problem 30P

The significance of the final nucleus in the last step of the carbon cycle is that 612C is used as a catalyst.

Explanation of Solution

The steps of the carbon cycle reactions in part (a)-(f) are

  1. (a) 11H+612C713N+γ
  2. (b) 713N613C+10e+ν
  3. (c) 11H+613C714N+γ
  4. (d) 11H+714N815O+γ
  5. (e) 815O715N+10e+ν
  6. (f) 11H+715N612C+24He

The overall reaction is 11H+612C+11H+11H+11H+210e612C+24He+7γ+ν. The positrons emitted in these reactions are annihilated immediately by free electrons, 10e++10e2γ.

Simplifying the equation, 411H+210e24He+ν. In the overall reaction, the nucleus F in part (f), 612C is used as a catalyst in the carbon cycle reaction.

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