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A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom is
- a)1
- b)4
- c)2
- d)3
Correct answer is option 'C'. Can you explain this answer?
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A positroniiun atom is system consisting of a position and an electron...
For posittronium atom reduced mass,
The Rydbery constant for positronium atom, RP is given by
...(1)
Now, the wavelength of Balmer first line
of positronium a tom is given by
....(2)
Similarly, for hydrogen atom, the wavelength of Balmer first line (ni = 3 to nf = 2) is given by
Now, the ratio of wavelengths of first line o f Balmer series o fpositronium a tom and hydrogen a tom is
The Rydbery constant for positronium atom, RP is given by
...(1)Now, the wavelength of Balmer first line
of positronium a tom is given by....(2)Similarly, for hydrogen atom, the wavelength of Balmer first line (ni = 3 to nf = 2) is given by
Now, the ratio of wavelengths of first line o f Balmer series o fpositronium a tom and hydrogen a tom is
Most Upvoted Answer
A positroniiun atom is system consisting of a position and an electron...
The Balmer series is a series of spectral lines in the visible region of the electromagnetic spectrum that are emitted by the hydrogen atom when an electron transitions from higher energy levels to the second energy level (n=2). Similarly, positronium is a system consisting of a positron and an electron revolving around their common center of mass. The positron is the antiparticle of an electron.
1. Calculating the ratio of wavelengths:
To determine the ratio of the wavelengths of the first line of the Balmer series of positronium to that of hydrogen, we need to consider the energy levels involved in the transitions.
2. Energy levels of positronium:
In positronium, the energy levels are similar to the hydrogen atom. The energy levels in positronium can be represented by the equation: En = -13.6 eV / n^2, where n is the principal quantum number.
3. Energy levels of hydrogen:
In hydrogen, the energy levels are given by the equation: En = -13.6 eV / n^2.
4. First line of the Balmer series:
The first line of the Balmer series in hydrogen corresponds to the transition from the third energy level (n=3) to the second energy level (n=2).
5. Calculating the wavelength:
The wavelength of the first line of the Balmer series can be calculated using the Rydberg formula: 1/λ = R(1/2^2 - 1/3^2), where R is the Rydberg constant.
6. Comparing the energy levels:
Since both positronium and hydrogen have similar energy level equations, the transition from the third energy level (n=3) to the second energy level (n=2) will have the same energy difference in both systems.
7. Conclusion:
As the energy difference is the same for both positronium and hydrogen, the ratio of the wavelengths of the first line of the Balmer series of positronium to that of hydrogen will also be the same. Therefore, the correct answer is option 'C', which states that the ratio is 2.
1. Calculating the ratio of wavelengths:
To determine the ratio of the wavelengths of the first line of the Balmer series of positronium to that of hydrogen, we need to consider the energy levels involved in the transitions.
2. Energy levels of positronium:
In positronium, the energy levels are similar to the hydrogen atom. The energy levels in positronium can be represented by the equation: En = -13.6 eV / n^2, where n is the principal quantum number.
3. Energy levels of hydrogen:
In hydrogen, the energy levels are given by the equation: En = -13.6 eV / n^2.
4. First line of the Balmer series:
The first line of the Balmer series in hydrogen corresponds to the transition from the third energy level (n=3) to the second energy level (n=2).
5. Calculating the wavelength:
The wavelength of the first line of the Balmer series can be calculated using the Rydberg formula: 1/λ = R(1/2^2 - 1/3^2), where R is the Rydberg constant.
6. Comparing the energy levels:
Since both positronium and hydrogen have similar energy level equations, the transition from the third energy level (n=3) to the second energy level (n=2) will have the same energy difference in both systems.
7. Conclusion:
As the energy difference is the same for both positronium and hydrogen, the ratio of the wavelengths of the first line of the Balmer series of positronium to that of hydrogen will also be the same. Therefore, the correct answer is option 'C', which states that the ratio is 2.
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A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer?
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A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer?.
A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A positroniiun atom is system consisting of a position and an electron revolving about their common center of mass, which lies halfway between them. The ratio of the wavelength of the first line of the Balmer series of positroniumatomto the wavelength of the first line of the Balmer seiies of hydrogen atom isa)1b)4c)2d)3Correct answer is option 'C'. Can you explain this answer?.
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