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A 1.00 g marble is constrained to roll inside a tube of length L = 1.00 cm. The tube is capped at both ends. Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. and then Calculate the exitation energy required to promote the marble to the next available energy state.
and the exitation energy is A x 10-32 J. The value of A is.
  • a)
    1.23
  • b)
    3.12
  • c)
    9.98
  • d)
    4.69
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A 1.00 g marble is constrained to roll inside a tube of length L = 1.0...

Hence the value of A is 4.69
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Most Upvoted Answer
A 1.00 g marble is constrained to roll inside a tube of length L = 1.0...

Quantum Number Calculation:

- The energy of the marble in the tube can be represented by the equation: En = (n^2 * h^2) / (8mL^2)
- Given initial energy E = 1.00 mJ = 1.00 x 10^-3 J
- Substitute the values into the equation: 1.00 x 10^-3 = (n^2 * h^2) / (8mL^2)
- Since h (Planck's constant), m (mass of marble), and L (length of tube) are constants, we can simplify the equation to: n^2 = (8 * E * L^2) / h^2
- Calculate n: n = sqrt((8 * 1.00 x 10^-3 * 0.01) / (6.63 x 10^-34)^2) ≈ 4.69

Excitation Energy Calculation:

- To find the excitation energy required to promote the marble to the next available energy state, we need to calculate the energy difference between the current state (n) and the next state (n+1)
- The excitation energy (ΔE) can be calculated by the equation: ΔE = E(n+1) - En
- Substitute the values into the equation: ΔE = ([(n+1)^2 * h^2] / [8mL^2]) - (n^2 * h^2) / (8mL^2)
- Simplify the equation: ΔE = h^2 / (8mL^2) * [(n+1)^2 - n^2]
- Calculate ΔE: ΔE = 6.63 x 10^-34 / (8 * 1.00 x 10^-3 * 0.01) * [(4.69+1)^2 - 4.69^2] ≈ 4.69 x 10^-32 J

Therefore, the excitation energy required to promote the marble to the next available energy state is approximately 4.69 x 10^-32 J, which corresponds to option 'D'.
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A 1.00 g marble is constrained to roll inside a tube of length L = 1.00 cm. The tube is capped at both ends. Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. and then Calculate the exitation energy required to promote the marble to the next available energy state.and theexitation energy is A x 10-32J. The value of A is.a)1.23b)3.12c)9.98d)4.69Correct answer is option 'D'. Can you explain this answer?
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A 1.00 g marble is constrained to roll inside a tube of length L = 1.00 cm. The tube is capped at both ends. Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. and then Calculate the exitation energy required to promote the marble to the next available energy state.and theexitation energy is A x 10-32J. The value of A is.a)1.23b)3.12c)9.98d)4.69Correct answer is option 'D'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A 1.00 g marble is constrained to roll inside a tube of length L = 1.00 cm. The tube is capped at both ends. Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. and then Calculate the exitation energy required to promote the marble to the next available energy state.and theexitation energy is A x 10-32J. The value of A is.a)1.23b)3.12c)9.98d)4.69Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1.00 g marble is constrained to roll inside a tube of length L = 1.00 cm. The tube is capped at both ends. Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1.00 mJ. and then Calculate the exitation energy required to promote the marble to the next available energy state.and theexitation energy is A x 10-32J. The value of A is.a)1.23b)3.12c)9.98d)4.69Correct answer is option 'D'. Can you explain this answer?.
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