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Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength
90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n
is (hc = 1242 eV nm)
90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n
is (hc = 1242 eV nm)
Correct answer is '2'. Can you explain this answer?
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Consider a hydrogen atom with its electron in the nth orbital. An elec...
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Consider a hydrogen atom with its electron in the nth orbital. An elec...
Given data:
Wavelength of electromagnetic radiation, λ = 90 nm
Kinetic energy of ejected electron, KE = 10.4 eV
hc = 1242 eV nm
To find: Value of n in the hydrogen atom
Solution:
We know that the energy of the photon is given by the formula:
E = hc/λ
where,
h = Planck's constant = 6.626 x 10^-34 J s
c = speed of light = 3 x 10^8 m/s
λ = wavelength of the radiation
Let's first convert the wavelength given in nanometers to meters:
λ = 90 nm = 90 x 10^-9 m
Substituting the values in the formula, we get:
E = (6.626 x 10^-34 J s x 3 x 10^8 m/s) / (90 x 10^-9 m)
E = 2.21 x 10^-18 J
We know that the energy required to ionize a hydrogen atom from its nth energy level is given by:
En = -13.6/n^2 eV
where,
En = energy of the nth energy level
n = principal quantum number
To completely ionize the atom, the energy of the photon must be equal to or greater than the energy required to remove the electron from the atom.
So, we can write:
E ≥ En
Substituting the values, we get:
2.21 x 10^-18 J ≥ (-13.6/n^2) eV
Let's convert the kinetic energy of the ejected electron from eV to joules:
1 eV = 1.6 x 10^-19 J
KE = 10.4 eV = 1.6 x 10^-19 J x 10.4 = 1.664 x 10^-18 J
Now, using the above equation, we get:
1.664 x 10^-18 J ≥ (-13.6/n^2) eV
Dividing both sides by -13.6 eV, we get:
-1.224 x 10^-19 ≥ 1/n^2
Taking the reciprocal of both sides and multiplying by -1, we get:
n^2 ≥ 819.18
n ≥ √819.18
n ≥ 28.6
Since the value of n must be an integer, the only possible value of n is 2.
Therefore, the value of n in the hydrogen atom is 2.
Wavelength of electromagnetic radiation, λ = 90 nm
Kinetic energy of ejected electron, KE = 10.4 eV
hc = 1242 eV nm
To find: Value of n in the hydrogen atom
Solution:
We know that the energy of the photon is given by the formula:
E = hc/λ
where,
h = Planck's constant = 6.626 x 10^-34 J s
c = speed of light = 3 x 10^8 m/s
λ = wavelength of the radiation
Let's first convert the wavelength given in nanometers to meters:
λ = 90 nm = 90 x 10^-9 m
Substituting the values in the formula, we get:
E = (6.626 x 10^-34 J s x 3 x 10^8 m/s) / (90 x 10^-9 m)
E = 2.21 x 10^-18 J
We know that the energy required to ionize a hydrogen atom from its nth energy level is given by:
En = -13.6/n^2 eV
where,
En = energy of the nth energy level
n = principal quantum number
To completely ionize the atom, the energy of the photon must be equal to or greater than the energy required to remove the electron from the atom.
So, we can write:
E ≥ En
Substituting the values, we get:
2.21 x 10^-18 J ≥ (-13.6/n^2) eV
Let's convert the kinetic energy of the ejected electron from eV to joules:
1 eV = 1.6 x 10^-19 J
KE = 10.4 eV = 1.6 x 10^-19 J x 10.4 = 1.664 x 10^-18 J
Now, using the above equation, we get:
1.664 x 10^-18 J ≥ (-13.6/n^2) eV
Dividing both sides by -13.6 eV, we get:
-1.224 x 10^-19 ≥ 1/n^2
Taking the reciprocal of both sides and multiplying by -1, we get:
n^2 ≥ 819.18
n ≥ √819.18
n ≥ 28.6
Since the value of n must be an integer, the only possible value of n is 2.
Therefore, the value of n in the hydrogen atom is 2.
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Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. 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 Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer?.
Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. 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 Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer?.
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Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer?, a detailed solution for Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer? has been provided alongside types of Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of nis (hc = 1242 eV nm)Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an
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