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Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -
- a)first three Lyman lines, first two Balmer lines and first Paschen line
- b)first three Lyman lines only
- c)first two Balmer lines only
- d)none of the above
Correct answer is option 'A'. Can you explain this answer?
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Electrons accelerated from rest by a potential difference of 12.75 V, ...
E4 – E1 = – 0.85 eV – (–13.6 eV)
= 12.75 eV.
Possible emission of spectral lies
(i) First three lyman lines
(ii) First two Balmer lines
(iii) First paschen line
= 12.75 eV.
Possible emission of spectral lies
(i) First three lyman lines
(ii) First two Balmer lines
(iii) First paschen line
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Electrons accelerated from rest by a potential difference of 12.75 V, ...
Explanation:
Lyman Series:
The Lyman series corresponds to the electron transitions from higher energy levels to the n=1 energy level in a hydrogen atom. The wavelength of the spectral lines in the Lyman series can be calculated using the Rydberg formula:
1/λ = R_H (1 - 1/n^2)
where λ is the wavelength, R_H is the Rydberg constant for hydrogen (1.097 × 10^7 m^(-1)), and n is the principal quantum number.
The first three lines in the Lyman series correspond to n=2 to n=1, n=3 to n=1, and n=4 to n=1 transitions.
Balmer Series:
The Balmer series corresponds to the electron transitions from higher energy levels to the n=2 energy level in a hydrogen atom. The wavelength of the spectral lines in the Balmer series can also be calculated using the Rydberg formula:
1/λ = R_H (1 - 1/n^2)
The first two lines in the Balmer series correspond to n=3 to n=2 and n=4 to n=2 transitions.
Paschen Series:
The Paschen series corresponds to the electron transitions from higher energy levels to the n=3 energy level in a hydrogen atom. The wavelength of the spectral lines in the Paschen series can be calculated using the Rydberg formula:
1/λ = R_H (1 - 1/n^2)
The first line in the Paschen series corresponds to n=4 to n=3 transition.
Explanation of the answer:
When electrons are accelerated through a potential difference, they gain kinetic energy. The kinetic energy gained by an electron can be calculated using the formula:
KE = eV
where KE is the kinetic energy, e is the charge of an electron (1.6 × 10^(-19) C), and V is the potential difference.
In this case, the potential difference is given as 12.75 V. So, the kinetic energy gained by the electrons is:
KE = (1.6 × 10^(-19) C) × (12.75 V) = 2.04 × 10^(-18) J
Using the kinetic energy, we can calculate the maximum wavelength of the spectral lines that can be emitted by the electrons. The maximum wavelength is given by:
λ = hc/KE
where λ is the wavelength, h is the Planck's constant (6.63 × 10^(-34) J·s), c is the speed of light (3 × 10^8 m/s), and KE is the kinetic energy.
Substituting the values:
λ = (6.63 × 10^(-34) J·s × 3 × 10^8 m/s) / (2.04 × 10^(-18) J) = 9.72 × 10^(-8) m
Converting the wavelength to nanometers:
λ = 9.72 × 10^(-8) m × (10^9 nm/1 m) = 97.2 nm
The first three Lyman lines have wavelengths of 121.6 nm, 102.6 nm, and 97.2 nm. Since the maximum wavelength of 97.2 nm
Lyman Series:
The Lyman series corresponds to the electron transitions from higher energy levels to the n=1 energy level in a hydrogen atom. The wavelength of the spectral lines in the Lyman series can be calculated using the Rydberg formula:
1/λ = R_H (1 - 1/n^2)
where λ is the wavelength, R_H is the Rydberg constant for hydrogen (1.097 × 10^7 m^(-1)), and n is the principal quantum number.
The first three lines in the Lyman series correspond to n=2 to n=1, n=3 to n=1, and n=4 to n=1 transitions.
Balmer Series:
The Balmer series corresponds to the electron transitions from higher energy levels to the n=2 energy level in a hydrogen atom. The wavelength of the spectral lines in the Balmer series can also be calculated using the Rydberg formula:
1/λ = R_H (1 - 1/n^2)
The first two lines in the Balmer series correspond to n=3 to n=2 and n=4 to n=2 transitions.
Paschen Series:
The Paschen series corresponds to the electron transitions from higher energy levels to the n=3 energy level in a hydrogen atom. The wavelength of the spectral lines in the Paschen series can be calculated using the Rydberg formula:
1/λ = R_H (1 - 1/n^2)
The first line in the Paschen series corresponds to n=4 to n=3 transition.
Explanation of the answer:
When electrons are accelerated through a potential difference, they gain kinetic energy. The kinetic energy gained by an electron can be calculated using the formula:
KE = eV
where KE is the kinetic energy, e is the charge of an electron (1.6 × 10^(-19) C), and V is the potential difference.
In this case, the potential difference is given as 12.75 V. So, the kinetic energy gained by the electrons is:
KE = (1.6 × 10^(-19) C) × (12.75 V) = 2.04 × 10^(-18) J
Using the kinetic energy, we can calculate the maximum wavelength of the spectral lines that can be emitted by the electrons. The maximum wavelength is given by:
λ = hc/KE
where λ is the wavelength, h is the Planck's constant (6.63 × 10^(-34) J·s), c is the speed of light (3 × 10^8 m/s), and KE is the kinetic energy.
Substituting the values:
λ = (6.63 × 10^(-34) J·s × 3 × 10^8 m/s) / (2.04 × 10^(-18) J) = 9.72 × 10^(-8) m
Converting the wavelength to nanometers:
λ = 9.72 × 10^(-8) m × (10^9 nm/1 m) = 97.2 nm
The first three Lyman lines have wavelengths of 121.6 nm, 102.6 nm, and 97.2 nm. Since the maximum wavelength of 97.2 nm
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Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer?
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Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer?.
Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Electrons accelerated from rest by a potential difference of 12.75 V, are bombarded on a monoatomic hydrogen gas. Possible emission of spectral lines are -a)first three Lyman lines, first two Balmer lines and first Paschen lineb)first three Lyman lines onlyc)first two Balmer lines onlyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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