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In a hydrogen like sample electron is in 2nd excited state, the Binding energy of 4th state of this sample is 13.6 eV, then               
  • a)
     A 25 eV photon can set free the electron from the second excited state of this sample.               
  • b)
     3 different types of photon will be observed if electrons make transition up to ground state from the second excited state               
  • c)
     If 23 eV photon is used then K. E. of the-ejected electron is 1 eV.               
  • d)
    2nd line of Balmer series of this sample has same energy value as 1st excitation energy of H-atoms.
Correct answer is option 'A,B'. Can you explain this answer?
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Question: In a hydrogen-like sample, the electron is in the 2nd excited state. The binding energy of the 4th state of this sample is 13.6 eV. Determine whether the following statements are correct:

a) A 25 eV photon can set free the electron from the second excited state of this sample.
b) 3 different types of photons will be observed if electrons make a transition up to the ground state from the second excited state.
c) If a 23 eV photon is used, then the kinetic energy of the ejected electron is 1 eV.
d) The 2nd line of the Balmer series of this sample has the same energy value as the 1st excitation energy of H-atoms.

Answer:

a) A 25 eV photon can set free the electron from the second excited state of this sample.
To determine whether a 25 eV photon can set free the electron from the second excited state, we need to compare the energy of the photon with the binding energy of the second excited state.

The binding energy of the second excited state is given by the formula:
E2 = -13.6 eV / n^2, where n is the principal quantum number.
For the second excited state, n = 2, so the binding energy is:
E2 = -13.6 eV / 2^2 = -13.6 eV / 4 = -3.4 eV.

Since the binding energy of the second excited state is -3.4 eV, it means that it requires 3.4 eV of energy to remove the electron from this state. Therefore, a 25 eV photon can set free the electron from the second excited state because its energy is greater than the required energy of 3.4 eV.

b) 3 different types of photons will be observed if electrons make a transition up to the ground state from the second excited state.
When an electron transitions from a higher energy state to a lower energy state, it releases energy in the form of a photon. The energy of the photon emitted is equal to the difference in energy between the initial and final states.

In this case, the electron is transitioning from the second excited state (n = 2) to the ground state (n = 1). The energy difference between these two states is given by the formula:
ΔE = -13.6 eV * (1/n1^2 - 1/n2^2), where n1 = 1 and n2 = 2.

Plugging in the values, we get:
ΔE = -13.6 eV * (1/1^2 - 1/2^2) = -13.6 eV * (1 - 1/4) = -13.6 eV * (3/4) = -10.2 eV.

Therefore, the energy of the photons emitted during this transition will be 10.2 eV. Since there are three different possible transitions between the second excited state and the ground state (from n = 2 to n = 1), we will observe three different types of photons.

c) If a 23 eV photon is used, then the kinetic energy of the ejected electron is 1 eV.
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In a hydrogen like sample electron is in 2nd excited state, the Binding energy of 4th state of this sample is 13.6 eV, thena)A 25 eV photon can set free the electron from the second excited state of this sample.b)3 different types of photon will be observed if electrons make transition up to ground state from the second excited statec)If 23 eV photon is used then K. E. of the-ejected electron is 1 eV.d)2nd line of Balmer series of this sample has same energy value as 1st excitation energy of H-atoms.Correct answer is option 'A,B'. Can you explain this answer?
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In a hydrogen like sample electron is in 2nd excited state, the Binding energy of 4th state of this sample is 13.6 eV, thena)A 25 eV photon can set free the electron from the second excited state of this sample.b)3 different types of photon will be observed if electrons make transition up to ground state from the second excited statec)If 23 eV photon is used then K. E. of the-ejected electron is 1 eV.d)2nd line of Balmer series of this sample has same energy value as 1st excitation energy of H-atoms.Correct answer is option 'A,B'. 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 In a hydrogen like sample electron is in 2nd excited state, the Binding energy of 4th state of this sample is 13.6 eV, thena)A 25 eV photon can set free the electron from the second excited state of this sample.b)3 different types of photon will be observed if electrons make transition up to ground state from the second excited statec)If 23 eV photon is used then K. E. of the-ejected electron is 1 eV.d)2nd line of Balmer series of this sample has same energy value as 1st excitation energy of H-atoms.Correct answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a hydrogen like sample electron is in 2nd excited state, the Binding energy of 4th state of this sample is 13.6 eV, thena)A 25 eV photon can set free the electron from the second excited state of this sample.b)3 different types of photon will be observed if electrons make transition up to ground state from the second excited statec)If 23 eV photon is used then K. E. of the-ejected electron is 1 eV.d)2nd line of Balmer series of this sample has same energy value as 1st excitation energy of H-atoms.Correct answer is option 'A,B'. Can you explain this answer?.
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