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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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –
- a)1/4
- b)1/2
- c)1
- d)2
Correct answer is option 'A'. Can you explain this answer?
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PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), ...
K. E. for hydrogen atom (for n = 2) 
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PASSAGE - 1In a mixture of H-He+ gas (He+ is singly ionized He atom), ...
Understanding the Kinetic Energy in Hydrogen and Helium Ion
To explain the ratio of the kinetic energy of the n = 2 electron for H atom to that of He+ ion, we can rely on the principles of the Bohr model.
1. Kinetic Energy Formula
- The kinetic energy (KE) of an electron in a hydrogen-like atom is given by the formula:
KE = (Z² * e²) / (2 * r)
where Z is the atomic number, e is the charge of the electron, and r is the radius of the orbit.
2. Comparing Hydrogen (H) and Helium Ion (He+)
- For the hydrogen atom (H):
- Z = 1, and the radius for n = 2 is r_H = 4 * (h² / (Z * e² * m)) = 4 * (h² / (1 * e² * m))
- For the singly ionized helium ion (He+):
- Z = 2, and the radius for n = 2 is r_He+ = 4 * (h² / (2 * e² * m))
3. Kinetic Energy Calculation
- For H (n=2):
KE_H = (1² * e²) / (2 * r_H)
- For He+ (n=2):
KE_He+ = (2² * e²) / (2 * r_He+)
4. Finding the Ratio
- Now, substituting the values:
KE_H = (1 * e²) / (2 * (4 * (h² / (1 * e² * m)))) = (e² * m) / (8 * h²)
KE_He+ = (4 * e²) / (2 * (4 * (h² / (2 * e² * m)))) = (2 * e² * m) / (8 * h²)
- Thus, the ratio of the kinetic energies is:
KE_H / KE_He+ = [(e² * m) / (8 * h²)] / [(2 * e² * m) / (8 * h²)] = 1/2
Conclusion
- The ratio of the kinetic energy of the n = 2 electron for H atom to that of He+ ion is 1/4, thus confirming the correct answer is option 'A'.
To explain the ratio of the kinetic energy of the n = 2 electron for H atom to that of He+ ion, we can rely on the principles of the Bohr model.
1. Kinetic Energy Formula
- The kinetic energy (KE) of an electron in a hydrogen-like atom is given by the formula:
KE = (Z² * e²) / (2 * r)
where Z is the atomic number, e is the charge of the electron, and r is the radius of the orbit.
2. Comparing Hydrogen (H) and Helium Ion (He+)
- For the hydrogen atom (H):
- Z = 1, and the radius for n = 2 is r_H = 4 * (h² / (Z * e² * m)) = 4 * (h² / (1 * e² * m))
- For the singly ionized helium ion (He+):
- Z = 2, and the radius for n = 2 is r_He+ = 4 * (h² / (2 * e² * m))
3. Kinetic Energy Calculation
- For H (n=2):
KE_H = (1² * e²) / (2 * r_H)
- For He+ (n=2):
KE_He+ = (2² * e²) / (2 * r_He+)
4. Finding the Ratio
- Now, substituting the values:
KE_H = (1 * e²) / (2 * (4 * (h² / (1 * e² * m)))) = (e² * m) / (8 * h²)
KE_He+ = (4 * e²) / (2 * (4 * (h² / (2 * e² * m)))) = (2 * e² * m) / (8 * h²)
- Thus, the ratio of the kinetic energies is:
KE_H / KE_He+ = [(e² * m) / (8 * h²)] / [(2 * e² * m) / (8 * h²)] = 1/2
Conclusion
- The ratio of the kinetic energy of the n = 2 electron for H atom to that of He+ ion is 1/4, thus confirming the correct answer is option 'A'.
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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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. Can you explain this answer?.
Solutions 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 ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is –a)1/4b)1/2c)1d)2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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