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A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]
- a)a
- b)b
- c)c
- d)d
Correct answer is '9'. Can you explain this answer?
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A single electron orbits round a stationary nucleus of charge Ze, wher...
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A single electron orbits round a stationary nucleus of charge Ze, wher...
To find the value of Z, we need to use the formula for the energy of an electron in the nth Bohr orbit:
En = -13.6 * (Z^2/n^2) eV
Given that it requires 47.2 eV to excite the electron from the second to the third orbit, we can set up an equation as follows:
E3 - E2 = 47.2 eV
-13.6 * (Z^2/3^2) - (-13.6 * (Z^2/2^2)) = 47.2
Simplifying the equation, we get:
-13.6 * ((Z^2/9) - (Z^2/4)) = 47.2
-13.6 * ((4Z^2 - 9Z^2)/36) = 47.2
-13.6 * (-5Z^2/36) = 47.2
Multiplying both sides by -36, we get:
5Z^2 = 47.2 * 36
Z^2 = (47.2 * 36)/5
Z^2 = 339.84
Taking the square root of both sides, we get:
Z ≈ 18.42
Therefore, the constant Z ≈ 18.42.
To find the required wavelength to ionize the atom from the ground state, we can use the Rydberg formula:
1/λ = RZ^2 * (1/n1^2 - 1/n2^2)
Where R is the Rydberg constant, Z is the charge of the nucleus, n1 is the initial orbit, and n2 is the final orbit.
Since we are ionizing the atom from the ground state (n1 = 1) to an unbound state (n2 = ∞), we can simplify the equation to:
1/λ = RZ^2
Given that the required wavelength is found to be 4n, we can set up an equation as follows:
1/(4n) = RZ^2
Simplifying the equation, we get:
λ = 1/(4nRZ^2)
Substituting the value of Z (18.42) and the Rydberg constant (R ≈ 1.097 × 10^7 m^-1), we get:
λ = 1/(4n * 1.097 × 10^7 * (18.42)^2) m
Therefore, the required wavelength of electromagnetic radiation to ionize the atom from the ground state is approximately 4n * 1.087 × 10^-9 m.
En = -13.6 * (Z^2/n^2) eV
Given that it requires 47.2 eV to excite the electron from the second to the third orbit, we can set up an equation as follows:
E3 - E2 = 47.2 eV
-13.6 * (Z^2/3^2) - (-13.6 * (Z^2/2^2)) = 47.2
Simplifying the equation, we get:
-13.6 * ((Z^2/9) - (Z^2/4)) = 47.2
-13.6 * ((4Z^2 - 9Z^2)/36) = 47.2
-13.6 * (-5Z^2/36) = 47.2
Multiplying both sides by -36, we get:
5Z^2 = 47.2 * 36
Z^2 = (47.2 * 36)/5
Z^2 = 339.84
Taking the square root of both sides, we get:
Z ≈ 18.42
Therefore, the constant Z ≈ 18.42.
To find the required wavelength to ionize the atom from the ground state, we can use the Rydberg formula:
1/λ = RZ^2 * (1/n1^2 - 1/n2^2)
Where R is the Rydberg constant, Z is the charge of the nucleus, n1 is the initial orbit, and n2 is the final orbit.
Since we are ionizing the atom from the ground state (n1 = 1) to an unbound state (n2 = ∞), we can simplify the equation to:
1/λ = RZ^2
Given that the required wavelength is found to be 4n, we can set up an equation as follows:
1/(4n) = RZ^2
Simplifying the equation, we get:
λ = 1/(4nRZ^2)
Substituting the value of Z (18.42) and the Rydberg constant (R ≈ 1.097 × 10^7 m^-1), we get:
λ = 1/(4n * 1.097 × 10^7 * (18.42)^2) m
Therefore, the required wavelength of electromagnetic radiation to ionize the atom from the ground state is approximately 4n * 1.087 × 10^-9 m.
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A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. Can you explain this answer?
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A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. 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 A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. Can you explain this answer?.
A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. 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 A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]a)ab)bc)cd)dCorrect answer is '9'. Can you explain this answer?.
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