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PASSAGE - 1
In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Q. The quantum number n of the state finally populated in He+ ions is –
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), ...
For hydrogen like atoms 
i.e., when hydrogen comes to ground state it will release 10.2 eV of energy.
E2 = – 13.6 eV
E3 = – 6.04 eV
E4 = – 3.4eV
E3 = – 6.04 eV
E4 = – 3.4eV
Here He+ ion is in the first excited state i.e., possessing energy – 13.6 eV. After receiving energy of + 10.2 eV from excited hydrogen atom on collision, the energy of electron will be (–13.6 + 10.2) eV = –3.4 eV.
This means that the electron will jump to n = 4.
Most Upvoted Answer
PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), ...
The quantum number n of the state finally populated in He ions can be determined by considering the energy transfer from H atoms to He ions.
In the Bohr model, the energy levels of an atom are given by the formula:
E = -13.6/n^2
where E is the energy of the level and n is the principal quantum number.
Since H atoms transfer their total excitation energy to He ions, the energy transferred is equal to the difference in energy between the initial and final states of the He ions.
Let's assume that the initial state of the He ions is the ground state, which corresponds to n = 1.
The energy of the ground state of He ions is given by:
E1 = -13.6/1^2 = -13.6 eV
The final state of the He ions is excited, so the energy of the final state is greater than the energy of the ground state.
Let's assume the energy of the final state is E2 and the quantum number of the final state is n.
The energy difference is given by:
ΔE = E2 - E1
Since H atoms transfer their total excitation energy to He ions, the energy difference is equal to the total excitation energy of the H atoms.
Let's assume the total excitation energy of the H atoms is ΔE_H.
ΔE = ΔE_H
Using the formula for the energy levels of the Bohr model, we can write:
ΔE_H = -13.6/n_H^2
where n_H is the principal quantum number of the excited state of the H atoms.
Since H atoms are excited to their respective first excited states, we have:
n_H = 2
Substituting this value into the equation, we get:
ΔE_H = -13.6/2^2 = -13.6/4 = -3.4 eV
Since the energy difference ΔE is equal to the total excitation energy ΔE_H, we have:
ΔE = -3.4 eV
Now, we can find the quantum number n of the final state of the He ions by rearranging the equation for the energy levels of the Bohr model:
E2 = E1 + ΔE
E2 = -13.6 + (-3.4) = -17 eV
Using the formula for the energy levels, we can find the quantum number n:
-17 = -13.6/n^2
n^2 = -13.6/(-17)
n^2 = 0.8
n ≈ 0.89
Since the quantum number n must be a positive integer, the final state populated in He ions is not physically possible.
In the Bohr model, the energy levels of an atom are given by the formula:
E = -13.6/n^2
where E is the energy of the level and n is the principal quantum number.
Since H atoms transfer their total excitation energy to He ions, the energy transferred is equal to the difference in energy between the initial and final states of the He ions.
Let's assume that the initial state of the He ions is the ground state, which corresponds to n = 1.
The energy of the ground state of He ions is given by:
E1 = -13.6/1^2 = -13.6 eV
The final state of the He ions is excited, so the energy of the final state is greater than the energy of the ground state.
Let's assume the energy of the final state is E2 and the quantum number of the final state is n.
The energy difference is given by:
ΔE = E2 - E1
Since H atoms transfer their total excitation energy to He ions, the energy difference is equal to the total excitation energy of the H atoms.
Let's assume the total excitation energy of the H atoms is ΔE_H.
ΔE = ΔE_H
Using the formula for the energy levels of the Bohr model, we can write:
ΔE_H = -13.6/n_H^2
where n_H is the principal quantum number of the excited state of the H atoms.
Since H atoms are excited to their respective first excited states, we have:
n_H = 2
Substituting this value into the equation, we get:
ΔE_H = -13.6/2^2 = -13.6/4 = -3.4 eV
Since the energy difference ΔE is equal to the total excitation energy ΔE_H, we have:
ΔE = -3.4 eV
Now, we can find the quantum number n of the final state of the He ions by rearranging the equation for the energy levels of the Bohr model:
E2 = E1 + ΔE
E2 = -13.6 + (-3.4) = -17 eV
Using the formula for the energy levels, we can find the quantum number n:
-17 = -13.6/n^2
n^2 = -13.6/(-17)
n^2 = 0.8
n ≈ 0.89
Since the quantum number n must be a positive integer, the final state populated in He ions is not physically possible.
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PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?
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PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?.
PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?.
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PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?, a detailed solution for PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.Q. The quantum number n of the state finally populated in He+ ions is –a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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