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A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)
- a)9a0
- b)25a0
- c)4a0
- d)16a0
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A hydrogen atom, initially in the ground state is excited by absorbing...
Energy of photon = 12500/980 = 12.75eV
∴ Electron will excite to n= 4
Since 'R' ∝ n2
∴ Radius of atom will be 16a0
∴ Electron will excite to n= 4
Since 'R' ∝ n2
∴ Radius of atom will be 16a0
Most Upvoted Answer
A hydrogen atom, initially in the ground state is excited by absorbing...
To determine what happens to the hydrogen atom when it absorbs a photon of wavelength 980 nm, we need to consider the energy levels of the atom and the energy associated with the absorbed photon.
The energy of a photon can be calculated using the equation:
E = hc/λ
Where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the photon.
Plugging in the values, we can calculate the energy of the absorbed photon:
E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/980 x 10^-9 m
E ≈ 2.02 x 10^-19 J
Now, let's consider the energy levels of a hydrogen atom. The ground state of a hydrogen atom has an energy level of -13.6 eV. The energy levels of a hydrogen atom are given by the formula:
En = -13.6 eV/n^2
Where En is the energy of the nth energy level.
To find out which energy level the atom is excited to after absorbing the photon, we can equate the energy of the absorbed photon to the energy difference between the ground state and the excited state:
2.02 x 10^-19 J = -13.6 eV/n^2 - (-13.6 eV/1^2)
2.02 x 10^-19 J = -13.6 eV (1 - 1/n^2)
To solve this equation, we need to find the value of n. Rearranging the equation, we get:
1 - 1/n^2 = (2.02 x 10^-19 J)/(-13.6 eV)
Converting the energy from joules to electron volts:
(2.02 x 10^-19 J)/(1.602 x 10^-19 J/eV) ≈ -1.26 eV
Substituting this value back into the equation:
1 - 1/n^2 = -1.26 eV/(-13.6 eV)
1 - 1/n^2 ≈ 0.093
Solving for n^2:
1/n^2 ≈ 1 - 0.093
1/n^2 ≈ 0.907
Taking the reciprocal of both sides:
n^2 ≈ 1/0.907
n^2 ≈ 1.10
Taking the square root:
n ≈ 1.05
Therefore, the hydrogen atom is excited to the energy level n ≈ 1.05 after absorbing a photon of wavelength 980 nm.
The energy of a photon can be calculated using the equation:
E = hc/λ
Where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the photon.
Plugging in the values, we can calculate the energy of the absorbed photon:
E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/980 x 10^-9 m
E ≈ 2.02 x 10^-19 J
Now, let's consider the energy levels of a hydrogen atom. The ground state of a hydrogen atom has an energy level of -13.6 eV. The energy levels of a hydrogen atom are given by the formula:
En = -13.6 eV/n^2
Where En is the energy of the nth energy level.
To find out which energy level the atom is excited to after absorbing the photon, we can equate the energy of the absorbed photon to the energy difference between the ground state and the excited state:
2.02 x 10^-19 J = -13.6 eV/n^2 - (-13.6 eV/1^2)
2.02 x 10^-19 J = -13.6 eV (1 - 1/n^2)
To solve this equation, we need to find the value of n. Rearranging the equation, we get:
1 - 1/n^2 = (2.02 x 10^-19 J)/(-13.6 eV)
Converting the energy from joules to electron volts:
(2.02 x 10^-19 J)/(1.602 x 10^-19 J/eV) ≈ -1.26 eV
Substituting this value back into the equation:
1 - 1/n^2 = -1.26 eV/(-13.6 eV)
1 - 1/n^2 ≈ 0.093
Solving for n^2:
1/n^2 ≈ 1 - 0.093
1/n^2 ≈ 0.907
Taking the reciprocal of both sides:
n^2 ≈ 1/0.907
n^2 ≈ 1.10
Taking the square root:
n ≈ 1.05
Therefore, the hydrogen atom is excited to the energy level n ≈ 1.05 after absorbing a photon of wavelength 980 nm.
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A hydrogen atom, initially in the ground state is excited by absorbing...
Is option B is correct option.
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A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer?
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A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer?.
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV – Å)a)9a0b)25a0c)4a0d)16a0Correct answer is option 'D'. Can you explain this answer?.
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