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Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 is
- a)2
- b)5/2
- c)11/2
- d)25/4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Four particles of mass m each are inside a two dimensional square box ...
To find the minimum energy of the system, we need to consider the possible energy levels for the four particles inside the square box. Each particle can occupy a different energy level, and since each state is occupied by only one particle, we need to consider the number of available energy levels.
Number of available energy levels:
Since the particles are in a two-dimensional square box, the energy levels are given by the equation:
E = (n_x^2 + n_y^2) * (h^2 / (8mL^2))
where n_x and n_y are the quantum numbers representing the number of nodes in the x and y directions, respectively. The quantum numbers can take on values from 1 to infinity.
Since each particle can occupy a different energy level, the total number of available energy levels for the four particles is given by the product of the number of available energy levels for each particle:
Total number of available energy levels = (Number of available energy levels for one particle)^4
= [(1^2 + 1^2) * (h^2 / (8mL^2))]^4
= [(2h^2 / (8mL^2))]^4
= (h^8 / (16^4m^4L^8))
Minimum energy:
The minimum energy of the system is obtained when each particle occupies the lowest available energy level. Therefore, the minimum energy is given by:
Minimum energy = 4 * (1^2 + 1^2) * (h^2 / (8mL^2))
= 4 * (2h^2 / (8mL^2))
= 2 * (h^2 / (8mL^2))
= 2 * (h^2 / (mL^2)) * (1/4)
= (1/2) * (h^2 / (mL^2))
= 5/2 * (h^2 / (mL^2))
Therefore, the minimum energy of the system in units of h^2/mL^2 is 5/2. Hence, option B is the correct answer.
Number of available energy levels:
Since the particles are in a two-dimensional square box, the energy levels are given by the equation:
E = (n_x^2 + n_y^2) * (h^2 / (8mL^2))
where n_x and n_y are the quantum numbers representing the number of nodes in the x and y directions, respectively. The quantum numbers can take on values from 1 to infinity.
Since each particle can occupy a different energy level, the total number of available energy levels for the four particles is given by the product of the number of available energy levels for each particle:
Total number of available energy levels = (Number of available energy levels for one particle)^4
= [(1^2 + 1^2) * (h^2 / (8mL^2))]^4
= [(2h^2 / (8mL^2))]^4
= (h^8 / (16^4m^4L^8))
Minimum energy:
The minimum energy of the system is obtained when each particle occupies the lowest available energy level. Therefore, the minimum energy is given by:
Minimum energy = 4 * (1^2 + 1^2) * (h^2 / (8mL^2))
= 4 * (2h^2 / (8mL^2))
= 2 * (h^2 / (8mL^2))
= 2 * (h^2 / (mL^2)) * (1/4)
= (1/2) * (h^2 / (mL^2))
= 5/2 * (h^2 / (mL^2))
Therefore, the minimum energy of the system in units of h^2/mL^2 is 5/2. Hence, option B is the correct answer.
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Community Answer
Four particles of mass m each are inside a two dimensional square box ...
correct answer is B.
so according to problem each state can occupied by only one particle. so 4 particles occupy 4 different states . To calculate minimum energy we will take 4 least energy levels . for clearance i have uploaded a photo
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Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer?
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Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer?.
Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one particle, the minimum energy of the system in units of h2/mL2 isa)2b)5/2c)11/2d)25/4Correct answer is option 'B'. Can you explain this answer?.
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