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A free electron moving in one-dimension was emitted from Zn metal surface after exposure to UV...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along say the x-direction on (a) The time-independent Schrödinger equation is Αψη (x)-Εηψη (x), where is the Hamiltonian (total energy) operator, and ψη (x) are the electron wave functions associated with energies En Assuming the electron's energy entirely comprises kinetic energy (as it is 'free' there is no potential energy term), write down the Schrödinger equation given that the momentum operator in one- dimension is...
9. (15 points) Electrons are emitted from the surface of a metal when it's exposed to...
9. (15 points) Electrons are emitted from the surface of a metal when it's exposed to light. This is called the photoclectric effect. Each metal has a certain threshold frequency of light, below which nothing happens. Right at this threshold frequency, an electron is emitted. The binding energy of a metal is the minimum amount of energy required to remove an electron from the surface of the metal. The binding energy for lithium metal is 279.7 kJ/mol (that is, it...
1. A free particle of mass m moving from the left in one dimension scatters from...
1. A free particle of mass m moving from the left in one dimension scatters from the potential V(x) αδ(x). Suppose that the wave number of the particle is k and that α > 0. a. State the general form of the wave function including reflected and transmitted waves. b. Find the amplitude t of the transmitted wave in terms of α, k, m, and h. Find T
In the photoelectric effect experiment, a beam of light is shining on a metal surface and the electrons are emitted from the metal. One of the three key findings is that a minimum frequency of lig...
In the photoelectric effect experiment, a beam of light is shining on a metal surface and the electrons are emitted from the metal. One of the three key findings is that a minimum frequency of light is required for emission of electrons. This minimum frequency is found to be 5.5 × 1014 s-1 for an unknown metal. 4 Briefly describe the other two findings and draw a plot fo the KE of emitted electrons against light frequency. (a) (6 marks)...
Electrons are emitted from the surface of a metal when it's exposed to light. This is...
Electrons are emitted from the surface of a metal when it's exposed to light. This is called the photoelectric effect. Each metal has a certain threshold frequency of light, below which nothing happens. Right at this threshold frequency, an electron is emitted. Above this frequency, the electron is emitted and the extra energy is transferred to the electron. The equation for this phenomenon is KE=hν−hν0KE=hν−hν0 where KEKEKE is the kinetic energy of the emitted electron, h=6.63×10−34J⋅sh=6.63×10−34J⋅s is Planck's constant, ννnu...
A particle moving in one dimension is described by the wave function ...
A particle moving in one dimension is described by the wave function$$ \psi(x)=\left\{\begin{array}{ll} A e^{-\alpha x}, & x \geq 0 \\ B e^{\alpha x}, & x<0 \end{array}\right. $$where \(\alpha=4.00 \mathrm{~m}^{-1}\). (a) Determine the constants \(A\) and \(B\) so that the wave function is continuous and normalized. (b) Calculate the probability of finding the particle in each of the following regions: (i) within \(0.10 \mathrm{~m}\) of the origin, (ii) on the left side of the origin.
Calculate the kinetic energy in units of electron volts for an electron emitted from a surface...
Calculate the kinetic energy in units of electron volts for an electron emitted from a surface with a work function of 1.5 eV that has been illuminated with632.8-nm (red) helium neon laser, such as those used in a supermarket scanner. Perform the same calculation for a 543.5-nm (green) helium-neon laser.
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are...
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are positive real constants. At t = π/(6ω) what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum? Express your answer in terms of k.
Consider free electron gas model in metal and an atom can be viewed as a number...
Consider free electron gas model in metal and an atom can be viewed as a number of electrons moving around a positively charged nucleus. Use the model of a particle in a box to estimate the energy (in eV) required to raise an atomic electron from the state n=1 to the state n=3, assuming the atom has a radius of 2Å.
A uniform ultraviolet light source shines on two metal plates causing electrons to be emitted from...
A uniform ultraviolet light source shines on two metal plates causing electrons to be emitted from each plate. Plate A emits twice as many electrons as plate B. However, the electrons emitted from plate B have a higher maximum velocity. Which of the following describes a plausible explanation for the differences in electron emission? (Select two answers.) A) Plate A must have a larger work function than plate B. B) The higher velocity electrons in case B would be produced...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along say the x-direction on (a) The time-independent Schrödinger equation is Αψη (x)-Εηψη (x), where is the Hamiltonian (total energy) operator, and ψη (x) are the electron wave functions associated with energies En Assuming the electron's energy entirely comprises kinetic energy (as it is 'free' there is no potential energy term), write down the Schrödinger equation given that the momentum operator in one- dimension is...
9. (15 points) Electrons are emitted from the surface of a metal when it's exposed to light. This is called the photoclectric effect. Each metal has a certain threshold frequency of light, below which nothing happens. Right at this threshold frequency, an electron is emitted. The binding energy of a metal is the minimum amount of energy required to remove an electron from the surface of the metal. The binding energy for lithium metal is 279.7 kJ/mol (that is, it...
1. A free particle of mass m moving from the left in one dimension scatters from the potential V(x) αδ(x). Suppose that the wave number of the particle is k and that α > 0. a. State the general form of the wave function including reflected and transmitted waves. b. Find the amplitude t of the transmitted wave in terms of α, k, m, and h. Find T
In the photoelectric effect experiment, a beam of light is shining on a metal surface and the electrons are emitted from the metal. One of the three key findings is that a minimum frequency of light is required for emission of electrons. This minimum frequency is found to be 5.5 × 1014 s-1 for an unknown metal. 4 Briefly describe the other two findings and draw a plot fo the KE of emitted electrons against light frequency. (a) (6 marks)...
Consider free electron gas model in metal and an atom can be viewed as a number of electrons moving around a positively charged nucleus. Use the model of a particle in a box to estimate the energy (in eV) required to raise an atomic electron from the state n=1 to the state n=3, assuming the atom has a radius of 2Å.
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