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Particle in a box. (a) We have learned that for a particle of mass m in 1-D infinite potential well of length L, the nth state satisfies psi _(n)(x)=Asin((npi x)/(L)),E_(n)=(h^(2)n^(2))/(8mL^(2)), for n=1,2,3,dots Show that A=sqrt((2)/(L)), for all values of n. [Hint: This integral expression (link)might be helpful.] (b) An electron is trapped in a one-dimensional infinite potential well that is 100pm wide. If the electron is in the ground state, what is the approximate probability that it can be detected in an interval of width Delta x=5.0pm centred at 25pm ? [Hint: This is a small enough width that you can take the probability density to be constant within the interval.] (c) What are the three longest wavelengths of light that the electron can absorb to be excited from the ground state? Illustrate the transitions in an energy diagram. (d) If the electron is in its third excited state, what is the probability that it can be found between 10pm and 40pm ? (e) If the electron is in its third excited state, what wavelengths of light can be emitted, including wavelengths involving more than one transition? Rank the wavelengths from longest to shortest, and illustrate the transitions in an energy diagram. Particle in a box (a) We have learned that for a particle of mass m in 1-D infinite potential well of length L the nth state satisfies h2n2 for n=1,2,3,. 8mL2 nTx 1n(x)= Asin E, Show that A = /2/L, for all values of n. [Hint: This integral expression (link )might be helpful.] (b) An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide If the electron is in the ground state, what is the approximate probability that it can be detected in an interval of width x = 5.0 pm centred at 25 pm? [Hint: This is a small enough width that you can take the probability density to be constant within the interval.] (c) What are the three longest wavelengths of light that the electron can absorb to be excited from the ground state? Illustrate the transitions in an energy diagram. (d) If the electron is in its third excited state, what is the probability that it can be found between 10 pm and 40 pm? (e) If the electron is in its third excited state, what wavelengths of light can be emitted including wavelengths involving more than one transition? Rank the wavelengths from longest to shortest, and illustrate the transitions in an energy diagram

          Particle in a box.
(a) We have learned that for a particle of mass m in 1-D infinite potential well of length L, the nth state satisfies
psi _(n)(x)=Asin((npi x)/(L)),E_(n)=(h^(2)n^(2))/(8mL^(2)), for n=1,2,3,dots
Show that A=sqrt((2)/(L)), for all values of n. [Hint: This integral expression (link)might be helpful.]
(b) An electron is trapped in a one-dimensional infinite potential well that is 100pm wide. If the electron is in the ground state, what is the approximate probability that it can be detected in an interval of width Delta x=5.0pm centred at 25pm ? [Hint: This is a small enough width that you can take the probability density to be constant within the interval.]
(c) What are the three longest wavelengths of light that the electron can absorb to be excited from the ground state? Illustrate the transitions in an energy diagram.
(d) If the electron is in its third excited state, what is the probability that it can be found between 10pm and 40pm ?
(e) If the electron is in its third excited state, what wavelengths of light can be emitted, including wavelengths involving more than one transition? Rank the wavelengths from longest to shortest, and illustrate the transitions in an energy diagram.
Particle in a box
(a) We have learned that for a particle of mass m in 1-D infinite potential well of length L the nth state satisfies
h2n2 for n=1,2,3,. 8mL2
nTx 1n(x)= Asin
E,
Show that A = /2/L, for all values of n. [Hint: This integral expression (link )might be helpful.]
(b) An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide
If the electron is in the ground state, what is the approximate probability that it can be detected in an interval of width x = 5.0 pm centred at 25 pm? [Hint: This is a small enough width that you can take the probability density to be constant within the interval.]
(c) What are the three longest wavelengths of light that the electron can absorb to be excited from the ground state? Illustrate the transitions in an energy diagram.
(d) If the electron is in its third excited state, what is the probability that it can be found between 10 pm and 40 pm?
(e) If the electron is in its third excited state, what wavelengths of light can be emitted including wavelengths involving more than one transition? Rank the wavelengths from longest to shortest, and illustrate the transitions in an energy diagram

particle in a box a we have learned that for a particle of mass m in 1 d infinite potential well of length l the nth state satisfies psi nxasinnpi xlenh2n28ml2 for n123dots show that asqrt 22766

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