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An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.?
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An electron in a one dimensional box of width 1A• undergoes a transiti...
Calculating the Transition Energy
To calculate the transition energy, we need to use the formula:
E = (n^2 * h^2) / (8*m*L^2)
where E is the energy of the state, n is the quantum number of the state (n=1 for the ground state and n=2 for the first excited state), h is Planck's constant, m is the mass of the electron, and L is the width of the box.
Substituting the Values
Substituting the given values, we get:
For the ground state (n=1):
E1 = (1^2 * h^2) / (8*m*L^2)
E1 = (1 * 6.626 x 10^-34 J s)^2 / (8 * 9.109 x 10^-31 kg * (1 x 10^-10 m)^2)
E1 = 3.38 x 10^-18 J
For the first excited state (n=2):
E2 = (2^2 * h^2) / (8*m*L^2)
E2 = (4 * 6.626 x 10^-34 J s)^2 / (8 * 9.109 x 10^-31 kg * (1 x 10^-10 m)^2)
E2 = 1.35 x 10^-17 J
Converting Joules to Electron Volts
To convert the energy from Joules to electron volts (eV), we need to divide the energy by the elementary charge (e):
1 eV = 1.602 x 10^-19 J
Therefore, the transition energy is:
E2 - E1 = (1.35 x 10^-17 J) - (3.38 x 10^-18 J)
E2 - E1 = 9.72 x 10^-18 J
E2 - E1 = 60.6 eV (approx.)
Thus, the transition energy from the ground state to the first excited state is approximately 60.6 eV.
To calculate the transition energy, we need to use the formula:
E = (n^2 * h^2) / (8*m*L^2)
where E is the energy of the state, n is the quantum number of the state (n=1 for the ground state and n=2 for the first excited state), h is Planck's constant, m is the mass of the electron, and L is the width of the box.
Substituting the Values
Substituting the given values, we get:
For the ground state (n=1):
E1 = (1^2 * h^2) / (8*m*L^2)
E1 = (1 * 6.626 x 10^-34 J s)^2 / (8 * 9.109 x 10^-31 kg * (1 x 10^-10 m)^2)
E1 = 3.38 x 10^-18 J
For the first excited state (n=2):
E2 = (2^2 * h^2) / (8*m*L^2)
E2 = (4 * 6.626 x 10^-34 J s)^2 / (8 * 9.109 x 10^-31 kg * (1 x 10^-10 m)^2)
E2 = 1.35 x 10^-17 J
Converting Joules to Electron Volts
To convert the energy from Joules to electron volts (eV), we need to divide the energy by the elementary charge (e):
1 eV = 1.602 x 10^-19 J
Therefore, the transition energy is:
E2 - E1 = (1.35 x 10^-17 J) - (3.38 x 10^-18 J)
E2 - E1 = 9.72 x 10^-18 J
E2 - E1 = 60.6 eV (approx.)
Thus, the transition energy from the ground state to the first excited state is approximately 60.6 eV.
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An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.?
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An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.?.
An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron in a one dimensional box of width 1A• undergoes a transition from the ground state (n=1) to first excited state (n=2).calculate the transition energy in eV.?.
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