When a particle is restricted to move aong `x`axis between `x =0` and `x = a`, where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends `x = 0` and `x = a`. The wavelength of this standing wave is realated to the linear momentum `p` of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as `E = (p^(2))/(2m)`. Thus, the energy of the particle can be denoted by a quantum number `'n'` taking values `1,2,3,"......."`(`n=1`, called the ground state) corresponding to the number of loop in the standing wave.
Use the model decribed above to answer the following three questions for a particle moving in the line `x = 0` to `x =a`. Take `h = 6.6 xx 10^(-34) J s` and `e = 1.6 xx 10^(-19) C`.
The allowed energy for the particle for a particular value of n is proportional to
When a particle is restricted to move aong `x`axis between `x =0` and `x = a`, where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends `x = 0` and `x = a`. The wavelength of this standing wave is realated to the linear momentum `p` of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as `E = (p^(2))/(2m)`. Thus, the energy of the particle can be denoted by a quantum number `'n'` taking values `1,2,3,"......."`(`n=1`, called the ground state) corresponding to the number of loop in the standing wave.
Use the model decribed above to answer the following three questions for a particle moving in the line `x = 0` to `x =a`. Take `h = 6.6 xx 10^(-34) J s` and `e = 1.6 xx 10^(-19) C`.
The allowed energy for the particle for a particular value of n is proportional to
Use the model decribed above to answer the following three questions for a particle moving in the line `x = 0` to `x =a`. Take `h = 6.6 xx 10^(-34) J s` and `e = 1.6 xx 10^(-19) C`.
The allowed energy for the particle for a particular value of n is proportional to
A
`a^(-2)`
B
`a^(-3//2)`
C
`a^(-1)`
D
`a^(2)`
Text Solution
Verified by Experts
The correct Answer is:
A
`E=p^(2)/(2m)` …(i) `" "p=h/lambda` …(ii)
By equation (i) and (ii)
`E=h^(2)/(2mlambda^(2))implies (h^(2)(n^(2)))/(2m(4a^(2)))`
`[ :' (n lambda)/2=a` for stationary wave on string fixed at both end`] E prop a^(-2)`
By equation (i) and (ii)
`E=h^(2)/(2mlambda^(2))implies (h^(2)(n^(2)))/(2m(4a^(2)))`
`[ :' (n lambda)/2=a` for stationary wave on string fixed at both end`] E prop a^(-2)`
|
Topper's Solved these Questions
SIMPLE HARMONIC MOTION
ALLEN|Exercise Comprehension #4|3 VideosSIMPLE HARMONIC MOTION
ALLEN|Exercise Comprehension #5|2 VideosSIMPLE HARMONIC MOTION
ALLEN|Exercise Comprehension #2|3 VideosRACE
ALLEN|Exercise Basic Maths (Wave Motion & Dopplers Effect) (Stationary waves & doppler effect, beats)|25 VideosTEST PAPER
ALLEN|Exercise PHYSICS|4 Videos
Similar Questions
Explore conceptually related problems
When a particle is restricted to move along x-axis between x=0 and x=a , where alpha if of nenometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x=0 and x=a . The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as E=(p^2)/(2m) . Thus the energy of the particle can be denoted by a quantum number n taking values 1,2,3, ...( n=1 , called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving along the line from x=0 to x=alpha . Take h=6.6xx10^(-34)Js and e=1.6xx10^(-19) C. Q. The allowed energy for the particle for a particular value of n is proportional to
When a particle is restricted to move along x-axis between x=0 and x=a , where alpha if of nenometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x=0 and x=a . The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as E=(p^2)/(2m) . Thus the energy of the particle can be denoted by a quantum number n taking values 1,2,3, ...( n=1 , called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving along the line from x=0 to x=alpha . Take h=6.6xx10^(-34)Js and e=1.6xx10^(-19) C Q. The speed of the particle that can take discrete values is proportional to
Knowledge Check
When a particle is restricted to move aong x axis between x =0 and x = a , where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a . The wavelength of this standing wave is realated to the linear momentum p of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as E = (p^(2))/(2m) . Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1,2,3,"......." ( n=1 , called the ground state) corresponding to the number of loop in the standing wave. Use the model decribed above to answer the following three questions for a particle moving in the line x = 0 to x =a . Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19) C . The speed of the particle, that can take disrete values, is proportional to
When a particle is restricted to move aong x axis between x =0 and x = a , where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a . The wavelength of this standing wave is realated to the linear momentum p of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as E = (p^(2))/(2m) . Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1,2,3,"......." ( n=1 , called the ground state) corresponding to the number of loop in the standing wave. Use the model decribed above to answer the following three questions for a particle moving in the line x = 0 to x =a . Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19) C . The speed of the particle, that can take disrete values, is proportional to
A
`n^(3//2)`
B
`n^(-1)`
C
`n^(-1//2)`
D
`n`
When a particle is restricted to move aong x axis between x =0 and x = a , where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a . The wavelength of this standing wave is realated to the linear momentum p of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as E = (p^(2))/(2m) . Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1,2,3,"......." ( n=1 , called the ground state) corresponding to the number of loop in the standing wave. Use the model decribed above to answer the following three questions for a particle moving in the line x = 0 to x =a . Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19) C . If the mass of the particle is m = 1.0 xx 10^(-30) kg and a = 6.6 nm , the energy of the particle in its ground state is closet to
When a particle is restricted to move aong x axis between x =0 and x = a , where a is of nanometer dimension. Its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a . The wavelength of this standing wave is realated to the linear momentum p of the particle according to the de Breogile relation. The energy of the particl e of mass m is reelated to its linear momentum as E = (p^(2))/(2m) . Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1,2,3,"......." ( n=1 , called the ground state) corresponding to the number of loop in the standing wave. Use the model decribed above to answer the following three questions for a particle moving in the line x = 0 to x =a . Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19) C . If the mass of the particle is m = 1.0 xx 10^(-30) kg and a = 6.6 nm , the energy of the particle in its ground state is closet to
A
`0.8 meV`
B
`8 meV`
C
`80 meV`
D
`800 meV`
When a particle is restricted to move along x- axis between x = 0 and x = 4 whwre a is opf nanometer demension , its energy can take only certain spscfic values . The allowed energies of the particles only in such a restiricted regain , correspond to the formation of standing wave with nodes at its end x = 0 and x = a .The wavelength of this standing wave is related to the linear momentum p of the paarticle according to the de Broglie relation .The energy of the particle of mass m is reated to its linear momentum as E = (p^(2))/(2m) . thus , the energy of the particle can be denoted by a quantum number n taking value 1,2,3,....(n= 1, called the ground state) corresponding to the number of loops in the standing wave use the model described above to answer the following there question for a particle moving in the line x = 0 to x = a Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19)C The alloewd energy for the particle for a particular value of n is proportional to
When a particle is restricted to move along x- axis between x = 0 and x = 4 whwre a is opf nanometer demension , its energy can take only certain spscfic values . The allowed energies of the particles only in such a restiricted regain , correspond to the formation of standing wave with nodes at its end x = 0 and x = a .The wavelength of this standing wave is related to the linear momentum p of the paarticle according to the de Broglie relation .The energy of the particle of mass m is reated to its linear momentum as E = (p^(2))/(2m) . thus , the energy of the particle can be denoted by a quantum number n taking value 1,2,3,....(n= 1, called the ground state) corresponding to the number of loops in the standing wave use the model described above to answer the following there question for a particle moving in the line x = 0 to x = a Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19)C The alloewd energy for the particle for a particular value of n is proportional to
A
`a^(-2)`
B
`a^(-3//2)`
C
`a^(-1)`
D
`a^(2)`
Similar Questions
Explore conceptually related problems
When a particle is restricted to move along x-axis between x=0 and x=a , where alpha if of nenometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x=0 and x=a . The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as E=(p^2)/(2m) . Thus the energy of the particle can be denoted by a quantum number n taking values 1,2,3, ...( n=1 , called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving along the line from x=0 to x=alpha . Take h=6.6xx10^(-34)Js and e=1.6xx10^(-19) C. Q. If the mass of the particle is m=1.0xx10^(-30) kg and alpha=6.6nm , the energy of the particle in its ground state is closest to
When a particle is restricted to move along x- axis between x = 0 and x = 4 whwre a is opf nanometer demension , its energy can take only certain spscfic values . The allowed energies of the particles only in such a restiricted regain , correspond to the formation of standing wave with nodes at its end x = 0 and x = a .The wavelength of this standing wave is related to the linear momentum p of the paarticle according to the de Broglie relation .The energy of the particle of mass m is reated to its linear momentum as E = (p^(2))/(2m) . thus , the energy of the particle can be denoted by a quantum number n taking value 1,2,3,....(n= 1, called the ground state) corresponding to the number of loops in the standing wave use the model described above to answer the following there question for a particle moving in the line x = 0 to x = a Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19)C The speed of the particle , that can take discrete values, is propotional to
When a particle is restricted to move along x- axis between x = 0 and x = 4 whwre a is opf nanometer demension , its energy can take only certain spscfic values . The allowed energies of the particles only in such a restiricted regain , correspond to the formation of standing wave with nodes at its end x = 0 and x = a .The wavelength of this standing wave is related to the linear momentum p of the paarticle according to the de Broglie relation .The energy of the particle of mass m is reated to its linear momentum as E = (p^(2))/(2m) . thus , the energy of the particle can be denoted by a quantum number n taking value 1,2,3,....(n= 1, called the ground state) corresponding to the number of loops in the standing wave use the model described above to answer the following there question for a particle moving in the line x = 0 to x = a Take h = 6.6 xx 10^(-34) J s and e = 1.6 xx 10^(-19)C If the mass of the particle is m = 1.0 xx 10^(-30) kg and a= 6.6 nm the energyof the particle in its ground state is closest to
In a standing wave formed as a result of reflection from a surface, the ratio of the amplitude at an antinode to that at node is X. The fraction of energy that is reflected is
A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when