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How does the energy gap between successive energy levels in an atom vary from low to high n values:
- a)All energy gaps are the same
- b)The energy gap decreases as n increases
- c)The energy gap increases as n increases
- d)The energy gap changes unpredictably as n increases
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
How does the energy gap between successive energy levels in an atom va...
The further away an electron is from the nucleus, the less force it feels from the electron, so the less energy is needed to “pop it off” the atom. The value of the energy level is exactly this amount of energy so the smaller it is, the smaller the difference with neighboring levels will be.
Most Upvoted Answer
How does the energy gap between successive energy levels in an atom va...
Yes...its correct ...see the example for Hydrogen spectrum ..which is given in almost every book ..so compare the gaps between n=1 and n=2 , which is higher than n=2 to n=3 and so on... difference of lumen to balmar is greater than balmar to paschen ......and balmar to paschen is greater than paschen to brackett... hence its correct
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How does the energy gap between successive energy levels in an atom va...
Energy Gap between Successive Energy Levels in an Atom
In an atom, electrons are arranged in different energy levels or shells. These energy levels are represented by the principal quantum number (n) and are numbered as 1, 2, 3, and so on. The energy of an electron increases as the distance from the nucleus increases, and therefore, the energy levels are not equally spaced. The energy gap between successive energy levels in an atom varies from low to high values, and it is affected by the value of the principal quantum number (n).
Explanation
The energy of an electron in an atom is given by the expression:
E = -13.6/n^2 eV
where n is the principal quantum number and E is the energy of the electron in electron volts (eV). The negative sign in the expression indicates that the energy of the electron is lower than the energy of a free electron at rest.
As we move from one energy level to another, the energy gap between them changes. The energy gap between the first and second energy levels is greater than the energy gap between the second and third energy levels, and so on. This is because the energy of an electron in an atom is inversely proportional to the square of the principal quantum number (n). As n increases, the energy gap between successive energy levels decreases.
For example, the energy gap between the first and second energy levels is given by:
ΔE = E2 - E1 = (-13.6/2^2) - (-13.6/1^2) = -3.4 eV
The energy gap between the second and third energy levels is given by:
ΔE = E3 - E2 = (-13.6/3^2) - (-13.6/2^2) = -1.89 eV
As we can see, the energy gap between successive energy levels decreases as the value of n increases. This is because the energy levels become closer together as n increases, and therefore, the energy gap between them decreases.
Conclusion
In conclusion, the energy gap between successive energy levels in an atom varies from low to high values, and it decreases as the value of the principal quantum number (n) increases. This is because the energy of an electron in an atom is inversely proportional to the square of the principal quantum number (n).
In an atom, electrons are arranged in different energy levels or shells. These energy levels are represented by the principal quantum number (n) and are numbered as 1, 2, 3, and so on. The energy of an electron increases as the distance from the nucleus increases, and therefore, the energy levels are not equally spaced. The energy gap between successive energy levels in an atom varies from low to high values, and it is affected by the value of the principal quantum number (n).
Explanation
The energy of an electron in an atom is given by the expression:
E = -13.6/n^2 eV
where n is the principal quantum number and E is the energy of the electron in electron volts (eV). The negative sign in the expression indicates that the energy of the electron is lower than the energy of a free electron at rest.
As we move from one energy level to another, the energy gap between them changes. The energy gap between the first and second energy levels is greater than the energy gap between the second and third energy levels, and so on. This is because the energy of an electron in an atom is inversely proportional to the square of the principal quantum number (n). As n increases, the energy gap between successive energy levels decreases.
For example, the energy gap between the first and second energy levels is given by:
ΔE = E2 - E1 = (-13.6/2^2) - (-13.6/1^2) = -3.4 eV
The energy gap between the second and third energy levels is given by:
ΔE = E3 - E2 = (-13.6/3^2) - (-13.6/2^2) = -1.89 eV
As we can see, the energy gap between successive energy levels decreases as the value of n increases. This is because the energy levels become closer together as n increases, and therefore, the energy gap between them decreases.
Conclusion
In conclusion, the energy gap between successive energy levels in an atom varies from low to high values, and it decreases as the value of the principal quantum number (n) increases. This is because the energy of an electron in an atom is inversely proportional to the square of the principal quantum number (n).
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How does the energy gap between successive energy levels in an atom vary from low to high n values:a)All energy gaps are the sameb)The energy gap decreases as n increasesc)The energy gap increases as n increasesd)The energy gap changes unpredictably as n increasesCorrect answer is option 'B'. Can you explain this answer?
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