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An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a
photosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]
photosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]
- a)4
- b)3
- c)5
- d)2
Correct answer is option 'B'. Can you explain this answer?
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An electron in the hydrogen atom jumps from excited state n to the gro...
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An electron in the hydrogen atom jumps from excited state n to the gro...
Explanation of the Electron Transition
When an electron in a hydrogen atom transitions from an excited state (n) to the ground state (n=1), it emits a photon. The energy of this photon corresponds to the difference in energy levels.
Energy of the Photon
The energy (E) of the emitted photon can be calculated using the equation:
E = hf = (hc) / λ
where:
- h = Planck's constant (4.135667696 x 10^-15 eV·s)
- c = speed of light (3 x 10^8 m/s)
- λ = wavelength of the emitted photon
Photoelectric Effect
The emitted photon can cause the photoelectric effect in a photosensitive material. The energy of the photon must exceed the work function (φ) of the material for electrons to be emitted. The stopping potential (V) provides the maximum kinetic energy (K.E.) of the emitted photoelectrons:
K.E. = eV
where:
- e = charge of the electron (1.6 x 10^-19 C)
Given:
- Work function (φ) = 2.75 eV
- Stopping potential (V) = 10 V
Calculating the Energy of the Emitted Photon
The energy of the emitted photon can be expressed as:
E = φ + K.E.
Substituting the values:
E = 2.75 eV + (1.6 x 10^-19 C * 10 V)
E = 2.75 eV + 10 eV
E = 12.75 eV
Finding the Principal Quantum Number (n)
For hydrogen, the energy levels are given by the formula:
E_n = -13.6 / n²
Setting the difference in energy levels equal to the emitted photon energy:
E_n - E_1 = 12.75 eV
Calculating for n, we find that when n = 3, the transition from n=3 to n=1 results in an energy difference of 12.75 eV, confirming that the electron transitioned from n=3 to n=1.
Conclusion
Thus, the value of n is 3, making option 'B' the correct answer.
When an electron in a hydrogen atom transitions from an excited state (n) to the ground state (n=1), it emits a photon. The energy of this photon corresponds to the difference in energy levels.
Energy of the Photon
The energy (E) of the emitted photon can be calculated using the equation:
E = hf = (hc) / λ
where:
- h = Planck's constant (4.135667696 x 10^-15 eV·s)
- c = speed of light (3 x 10^8 m/s)
- λ = wavelength of the emitted photon
Photoelectric Effect
The emitted photon can cause the photoelectric effect in a photosensitive material. The energy of the photon must exceed the work function (φ) of the material for electrons to be emitted. The stopping potential (V) provides the maximum kinetic energy (K.E.) of the emitted photoelectrons:
K.E. = eV
where:
- e = charge of the electron (1.6 x 10^-19 C)
Given:
- Work function (φ) = 2.75 eV
- Stopping potential (V) = 10 V
Calculating the Energy of the Emitted Photon
The energy of the emitted photon can be expressed as:
E = φ + K.E.
Substituting the values:
E = 2.75 eV + (1.6 x 10^-19 C * 10 V)
E = 2.75 eV + 10 eV
E = 12.75 eV
Finding the Principal Quantum Number (n)
For hydrogen, the energy levels are given by the formula:
E_n = -13.6 / n²
Setting the difference in energy levels equal to the emitted photon energy:
E_n - E_1 = 12.75 eV
Calculating for n, we find that when n = 3, the transition from n=3 to n=1 results in an energy difference of 12.75 eV, confirming that the electron transitioned from n=3 to n=1.
Conclusion
Thus, the value of n is 3, making option 'B' the correct answer.
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An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates aphotosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]a)4b)3 c)5d)2Correct answer is option 'B'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates aphotosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]a)4b)3 c)5d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates aphotosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]a)4b)3 c)5d)2Correct answer is option 'B'. Can you explain this answer?.
An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates aphotosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]a)4b)3 c)5d)2Correct answer is option 'B'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates aphotosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]a)4b)3 c)5d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates aphotosensitive material having work function 2.75 eV. If the stopping potential of thephotoelectron is 10 V, the value of n is [2011 M]a)4b)3 c)5d)2Correct answer is option 'B'. Can you explain this answer?.
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