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The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will be
- a)28.4 MeV
- b)20.8 MeV
- c)27.3 MeV
- d)14.2 MeV
Correct answer is option 'A'. Can you explain this answer?
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The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u res...
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The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u res...
Calculation of Binding Energy of Helium Nucleus
Given:
Mass of neutron (mn) = 1.0087 a.m.u
Mass of proton (mp) = 1.0073 a.m.u
Mass of helium nucleus (mHe) = 4.0015 a.m.u
Step 1:
Determine the number of neutrons and protons in the helium nucleus.
Since the atomic number of helium is 2, the number of protons in the nucleus is 2.
Thus, the number of neutrons in the nucleus can be calculated as:
Number of neutrons = Mass number - Atomic number
= 4 - 2
= 2
Therefore, the helium nucleus contains 2 protons and 2 neutrons.
Step 2:
Calculate the mass defect (Δm) of the helium nucleus.
The mass defect is the difference between the mass of the individual nucleons (protons and neutrons) and the mass of the nucleus.
Δm = (2 × mp + 2 × mn) - mHe
= (2 × 1.0073 a.m.u + 2 × 1.0087 a.m.u) - 4.0015 a.m.u
= 0.0303 a.m.u
Step 3:
Calculate the binding energy (BE) of the helium nucleus.
The binding energy is the energy required to dissociate the nucleus into its individual nucleons.
BE = Δm × c²
where c is the speed of light.
BE = 0.0303 a.m.u × (1.66054 × 10^-27 kg/a.m.u) × (2.998 × 10^8 m/s)²
= 2.83 × 10^-12 kg × (9 × 10^16 m²/s²)
= 2.547 × 10^-5 J
Step 4:
Convert the binding energy into MeV.
1 eV = 1.602 × 10^-19 J
1 MeV = 1.602 × 10^-13 J
BE (in MeV) = (2.547 × 10^-5 J) / (1.602 × 10^-13 J/MeV)
= 0.159 MeV
Therefore, the binding energy of the helium nucleus is:
BE = 0.159 MeV/nucleon × 4 nucleons
= 0.636 MeV
Step 5:
Calculate the binding energy per nucleon.
The binding energy per nucleon is the binding energy divided by the number of nucleons.
Binding energy per nucleon = BE / number of nucleons
= 0.636 MeV / 4
= 0.159 MeV/nucleon
Therefore, the binding energy per nucleon of the helium nucleus is 0.159 MeV/nucleon.
Step 6:
Convert the binding energy per nucleon into MeV.
The binding energy per nucleon is usually expressed in MeV.
1 MeV/nucleon = 1.602 × 10^-13 J/nucleon
= (1.602 × 10^-13 J/nucleon) / (1.602 × 10^-19
Given:
Mass of neutron (mn) = 1.0087 a.m.u
Mass of proton (mp) = 1.0073 a.m.u
Mass of helium nucleus (mHe) = 4.0015 a.m.u
Step 1:
Determine the number of neutrons and protons in the helium nucleus.
Since the atomic number of helium is 2, the number of protons in the nucleus is 2.
Thus, the number of neutrons in the nucleus can be calculated as:
Number of neutrons = Mass number - Atomic number
= 4 - 2
= 2
Therefore, the helium nucleus contains 2 protons and 2 neutrons.
Step 2:
Calculate the mass defect (Δm) of the helium nucleus.
The mass defect is the difference between the mass of the individual nucleons (protons and neutrons) and the mass of the nucleus.
Δm = (2 × mp + 2 × mn) - mHe
= (2 × 1.0073 a.m.u + 2 × 1.0087 a.m.u) - 4.0015 a.m.u
= 0.0303 a.m.u
Step 3:
Calculate the binding energy (BE) of the helium nucleus.
The binding energy is the energy required to dissociate the nucleus into its individual nucleons.
BE = Δm × c²
where c is the speed of light.
BE = 0.0303 a.m.u × (1.66054 × 10^-27 kg/a.m.u) × (2.998 × 10^8 m/s)²
= 2.83 × 10^-12 kg × (9 × 10^16 m²/s²)
= 2.547 × 10^-5 J
Step 4:
Convert the binding energy into MeV.
1 eV = 1.602 × 10^-19 J
1 MeV = 1.602 × 10^-13 J
BE (in MeV) = (2.547 × 10^-5 J) / (1.602 × 10^-13 J/MeV)
= 0.159 MeV
Therefore, the binding energy of the helium nucleus is:
BE = 0.159 MeV/nucleon × 4 nucleons
= 0.636 MeV
Step 5:
Calculate the binding energy per nucleon.
The binding energy per nucleon is the binding energy divided by the number of nucleons.
Binding energy per nucleon = BE / number of nucleons
= 0.636 MeV / 4
= 0.159 MeV/nucleon
Therefore, the binding energy per nucleon of the helium nucleus is 0.159 MeV/nucleon.
Step 6:
Convert the binding energy per nucleon into MeV.
The binding energy per nucleon is usually expressed in MeV.
1 MeV/nucleon = 1.602 × 10^-13 J/nucleon
= (1.602 × 10^-13 J/nucleon) / (1.602 × 10^-19
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The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u res...
Binding energy=∆m×931.5Mev.....∆m is mass defect in amu
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The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer?
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The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer?.
The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The masses of neutron and proton are 1.0087 a.m.u and 1.0073 a.m.u respectively. If the neutrons and protons combine to form a helium nucleus of mass 4.0015 a.m.u. The binding energy of the helium will bea)28.4 MeVb)20.8 MeVc)27.3 MeVd)14.2 MeVCorrect answer is option 'A'. Can you explain this answer?.
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