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The maximum number of electrons that can be accomodate in the nth level is–
- a)n2
- b)2n2
- c)4n2
- d)n
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The maximum number of electrons that can be accomodate in the nth leve...
According to the question, we need to determine the maximum number of electrons that can be accommodated in the nth level.
To solve this problem, we can use the formula for the maximum number of electrons in a specific energy level. The formula is given by:
Maximum number of electrons = 2n^2
Where:
- n represents the energy level or the principal quantum number.
Let's break down the solution into steps:
Step 1: Substitute the value of n into the formula.
- We are given the value of n as the nth level.
Step 2: Calculate the maximum number of electrons.
- Square the value of n (n^2).
- Multiply the squared value by 2 (2n^2).
Step 3: Determine the final answer.
- The maximum number of electrons that can be accommodated in the nth level is equal to the result obtained from step 2.
Therefore, the correct answer is option B: 2n^2.
To solve this problem, we can use the formula for the maximum number of electrons in a specific energy level. The formula is given by:
Maximum number of electrons = 2n^2
Where:
- n represents the energy level or the principal quantum number.
Let's break down the solution into steps:
Step 1: Substitute the value of n into the formula.
- We are given the value of n as the nth level.
Step 2: Calculate the maximum number of electrons.
- Square the value of n (n^2).
- Multiply the squared value by 2 (2n^2).
Step 3: Determine the final answer.
- The maximum number of electrons that can be accommodated in the nth level is equal to the result obtained from step 2.
Therefore, the correct answer is option B: 2n^2.
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The maximum number of electrons that can be accomodate in the nth leve...
Maximum Number of Electrons in the nth Level
The configuration of electrons in an atom is determined by quantum mechanics, and each electron occupies an energy level or shell around the nucleus.
Electron Capacity Formula
- The maximum number of electrons that can be accommodated in the nth energy level is given by the formula: 2n².
- Here, n represents the principal quantum number, which indicates the shell or energy level.
Explanation of the Formula
- Principal Quantum Number (n):
- It indicates the energy level of an electron in an atom.
- n can take positive integer values: 1, 2, 3, etc.
- Derivation of 2n²:
- Each energy level can contain sub-levels (s, p, d, f).
- The number of orbitals in each sub-level increases with n.
- Each orbital can hold a maximum of 2 electrons (due to the Pauli Exclusion Principle).
- Therefore, the total number of electrons in the nth level can be calculated as:
- s sub-level (1 orbital): 2 electrons
- p sub-level (3 orbitals): 6 electrons
- d sub-level (5 orbitals): 10 electrons
- f sub-level (7 orbitals): 14 electrons
Combining these gives:
- Total = 2 + 6 + 10 + 14 = 2n² for n = 1, 2, 3, etc.
Conclusion
- Hence, the correct answer is option B: 2n², indicating that as the principal quantum number increases, the capacity for electrons grows significantly, leading to the structure of the periodic table and chemical properties of elements.
The configuration of electrons in an atom is determined by quantum mechanics, and each electron occupies an energy level or shell around the nucleus.
Electron Capacity Formula
- The maximum number of electrons that can be accommodated in the nth energy level is given by the formula: 2n².
- Here, n represents the principal quantum number, which indicates the shell or energy level.
Explanation of the Formula
- Principal Quantum Number (n):
- It indicates the energy level of an electron in an atom.
- n can take positive integer values: 1, 2, 3, etc.
- Derivation of 2n²:
- Each energy level can contain sub-levels (s, p, d, f).
- The number of orbitals in each sub-level increases with n.
- Each orbital can hold a maximum of 2 electrons (due to the Pauli Exclusion Principle).
- Therefore, the total number of electrons in the nth level can be calculated as:
- s sub-level (1 orbital): 2 electrons
- p sub-level (3 orbitals): 6 electrons
- d sub-level (5 orbitals): 10 electrons
- f sub-level (7 orbitals): 14 electrons
Combining these gives:
- Total = 2 + 6 + 10 + 14 = 2n² for n = 1, 2, 3, etc.
Conclusion
- Hence, the correct answer is option B: 2n², indicating that as the principal quantum number increases, the capacity for electrons grows significantly, leading to the structure of the periodic table and chemical properties of elements.
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