Quantum Mechanics Answers

Due to collision of an of energy 22 eV with a hydrogen atom, the atom exited to the higher energy state and motion of electron is retarded. Immediately a photon of wavelength 1216 Å is emitted. What is the velocity of the electron after the collision?

P.S. Answer is 2.037 x 10^6 m/s

Solve the Schrödinger equation for a particle in a box with sides at 𝑥 = −𝐿 and 𝑥 = 𝐿. Determine the eigenvalues and the normalized eigenfunctions. 

Consider the function 𝜓(𝜃) of the angular variable 𝜃, restricted to the interval −𝜋 ≤ 𝜃 ≤ 𝜋. If the wave functions satisfy the condition 𝜓(𝜋) = 𝜓(−𝜋), show that the operator 𝐿 = ℏ / 𝑖. 𝑑 / 𝑑𝜃 has a real expectation value.

Show that for a one-dimensional square integrable wave function 𝜓(𝑥,𝑡), we have ∫ 𝑑𝑥 𝑗(𝑥) = < 𝑝 >/m where 𝑗(𝑥) is the probability current. Hint: Start from the definition of 𝑗(𝑥) and integrate it by parts.

A ray of light of wavelength 36.5x10^-8 m and intensity of 10^-8 Wm^-2 is incident perpendicularly on a surface. Absorption coefficient of that surface is 0.8 and work function is 1.6eV. Calculate

(a) rate of production of electron from unit area

(b) absorbed energy per square meter

(c) kinetic energy of the produced electrons

Recall the Hadamard gate H

H that transforms from the {|0⟩,|1⟩}

{|0⟩,|1⟩} basis to the {|+⟩,|−⟩}

{|+⟩,|−⟩} basis. In outer product notation, this gate can be written as,

A Pelton wheel of 1.2 m mean bucket diameter works under a head of 650 m. The jet deflectionis 1650 and its relative velocity is reduced over the buckets by 15% due to friction. If the water isto leave the bucket without whirl, determine the rotational speed of the wheel. The coefficient ofvelocity is C, 50.98(a) 786.38 rpm(b) 1425.36 rpm(c) 320.2 rpm(d) 480.6 rpm
In the above problem, the ratio of bucket to jet speed can be calculated as(a) 0.1(b) 1.5(c) 0.45(d) 2.52
In the above problem, for a jet diameter of 100 cm, the impulsive force on a bucket of the Peltonwheel can be calculated as(a) 12.26 kN(b)62.36 kN(c) 32.36 kN(d) 94.26 kN

calculate the de Broglie wavelength of a free electron with an energy of 50 GeV

the work function of pure sodium is 2.75 eV. calculate the maximum kinetic energy of the photoelectrons that are split from sodium if given an ultraviolet radius with a wavelength of 200nm