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Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge −2e (e is the electronic charge). Apply the Bohr atom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and λo is the maximum wavelength of photon emitted then find the value of 20λoR.
Correct answer is '3'. Can you explain this answer?
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Consider a hypothetical atom made up of a proton and a hypothetical pa...
Rydberg constant for hydrogen atom is
So, Rydberg constant for this hypothetical atom is R' = R × 3 × 24 = 48R
For maximum wavelength emitted nf = 2 and ni = 3
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Consider a hypothetical atom made up of a proton and a hypothetical pa...
The problem involves a hypothetical atom consisting of a proton and a particle with three times the mass of an electron, but with a charge of 2e (where e is the electronic charge). We are asked to apply the Bohr atom model and consider all possible transitions of this hypothetical particle from higher energy levels to the first excited level.
1. Bohr Atom Model:
The Bohr atom model is a simplified model of the atom proposed by Niels Bohr in 1913. It considers electrons to orbit around the nucleus in discrete energy levels. The energy of these levels is determined by the angular momentum of the electron.
2. Transitions from Higher Energy Levels to First Excited Level:
In the Bohr atom model, electrons can transition from one energy level to another by absorbing or emitting photons. The energy difference between the initial and final energy levels is equal to the energy of the emitted or absorbed photon.
3. Energy Levels and Transitions:
In this hypothetical atom, the energy levels can be calculated using the formula:
E = -R/n^2
where E is the energy, R is the Rydberg constant, and n is the principal quantum number.
To find the possible transitions from higher energy levels to the first excited level (n = 2), we can calculate the energy differences for different values of n.
4. Calculating Energy Differences:
Let's consider a transition from the nth energy level to the first excited level (n = 2). The energy difference is given by:
ΔE = E_n - E_2
Substituting the values of E_n and E_2 from the formula, we get:
ΔE = -R/n^2 - (-R/2^2)
= -R(1/n^2 - 1/4)
5. Maximum Wavelength of Photon Emitted:
The maximum wavelength of the photon emitted (o) can be calculated using the formula:
o = c/ΔE
where c is the speed of light.
Substituting the value of ΔE, we get:
o = c/(-R(1/n^2 - 1/4))
6. Finding 20oR:
To find the value of 20oR, we need to substitute the value of o in the formula and multiply it by 20:
20oR = 20 * c/(-R(1/n^2 - 1/4))
7. Correct Answer:
The correct answer is given as 3. To confirm this, we need to calculate the value of 20oR using the above formula and the appropriate values for c and R.
1. Bohr Atom Model:
The Bohr atom model is a simplified model of the atom proposed by Niels Bohr in 1913. It considers electrons to orbit around the nucleus in discrete energy levels. The energy of these levels is determined by the angular momentum of the electron.
2. Transitions from Higher Energy Levels to First Excited Level:
In the Bohr atom model, electrons can transition from one energy level to another by absorbing or emitting photons. The energy difference between the initial and final energy levels is equal to the energy of the emitted or absorbed photon.
3. Energy Levels and Transitions:
In this hypothetical atom, the energy levels can be calculated using the formula:
E = -R/n^2
where E is the energy, R is the Rydberg constant, and n is the principal quantum number.
To find the possible transitions from higher energy levels to the first excited level (n = 2), we can calculate the energy differences for different values of n.
4. Calculating Energy Differences:
Let's consider a transition from the nth energy level to the first excited level (n = 2). The energy difference is given by:
ΔE = E_n - E_2
Substituting the values of E_n and E_2 from the formula, we get:
ΔE = -R/n^2 - (-R/2^2)
= -R(1/n^2 - 1/4)
5. Maximum Wavelength of Photon Emitted:
The maximum wavelength of the photon emitted (o) can be calculated using the formula:
o = c/ΔE
where c is the speed of light.
Substituting the value of ΔE, we get:
o = c/(-R(1/n^2 - 1/4))
6. Finding 20oR:
To find the value of 20oR, we need to substitute the value of o in the formula and multiply it by 20:
20oR = 20 * c/(-R(1/n^2 - 1/4))
7. Correct Answer:
The correct answer is given as 3. To confirm this, we need to calculate the value of 20oR using the above formula and the appropriate values for c and R.
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Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. Can you explain this answer?
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Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. 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 Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. Can you explain this answer?.
Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. 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 Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a hypothetical atom made up of a proton and a hypothetical particle of three times the mass of electron but having the charge 2e (e is the electronic charge). Apply the Bohratom model and consider all possible transitions of this hypothetical particle from the higher energy levels to the first excited level. If Rydberg constant for hydrogen atom is R and o is the maximum wavelength of photon emitted then find the value of 20oR.Correct answer is '3'. Can you explain this answer?.
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