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An election is confined in an infinite square well of width 10x10^-10 m. Calculate the energy & wavelength of the electron emitted when the proton undergoes a transition from the first excited state (n=2) to the ground state (n=1).
Correct answer is '201'. Can you explain this answer?
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An election is confined in an infinite square well of width 10x10^-10 ...
The energy of the particle in the box of width L is given by
λ = 201 fm
λ = 201 fm
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An election is confined in an infinite square well of width 10x10^-10 ...
The energy of a particle in an infinite square well is given by:
E = (n^2 * h^2) / (8 * m * L^2)
where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the width of the well.
In this case, L = 10x10^-10 m, so we can plug in the values:
E = (n^2 * h^2) / (8 * m * (10x10^-10)^2)
We don't know the quantum number or the mass of the particle, so we can't calculate the specific energy. However, we can make some general observations:
- The energy is proportional to the square of the quantum number. This means that higher energy levels require larger values of n.
- The energy is inversely proportional to the square of the width of the well. This means that a narrower well will have higher energy levels.
- The energy is inversely proportional to the mass of the particle. This means that lighter particles will have higher energy levels.
So, depending on the specific values of n and m, the energy could be very low or very high. But we can say for certain that the energy levels will be quantized (discrete), with larger gaps between levels for higher values of n.
E = (n^2 * h^2) / (8 * m * L^2)
where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the width of the well.
In this case, L = 10x10^-10 m, so we can plug in the values:
E = (n^2 * h^2) / (8 * m * (10x10^-10)^2)
We don't know the quantum number or the mass of the particle, so we can't calculate the specific energy. However, we can make some general observations:
- The energy is proportional to the square of the quantum number. This means that higher energy levels require larger values of n.
- The energy is inversely proportional to the square of the width of the well. This means that a narrower well will have higher energy levels.
- The energy is inversely proportional to the mass of the particle. This means that lighter particles will have higher energy levels.
So, depending on the specific values of n and m, the energy could be very low or very high. But we can say for certain that the energy levels will be quantized (discrete), with larger gaps between levels for higher values of n.
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An election is confined in an infinite square well of width 10x10^-10 m. Calculate the energy & wavelength of the electron emitted when the proton undergoes a transition from the first excited state (n=2) to the ground state (n=1).Correct answer is '201'. Can you explain this answer?
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