Quantum Mechanics Answers

Q1. Show that any solution of the time-independent Schrodinger equation with a symmetric potential is a linear combination of solutions of definite parity.

Q2. For a dissipative system given by a potential in the form 𝑉(𝑥) + 𝑖𝛼𝑊(𝑥) find the equation of continuity for quantum probability.

1)Suppose the temperature of a COVID positive patient is recorded as Tbody = 40°C. Determine the wavelength at which the radiation emitted from the body reaches its peak.

2) Derive the energy and wave function of a particle present in the n th state bounded in a length of ‘L’ subjected to boundary conditions 0 < x < L ?

3) An electron is bound in one dimensional potential well of width 0.2 nm. Find the energy value in eV of the third excited state.

4) Why uncertainty principle is not applicable to human? Electrons moving with a velocity of 4.5 × 105 m/s if this velocity is measured with an inaccuracy of 0.5 % then estimate the uncertainty in the position of an electron?

Calculate the maximum energy and the speed

of the emitted electrons when sodium is

illuminated by a radiation of wavelength

150nm. What is the least frequency of radiation

(threshold frequency) for which electrons are

emitted?

(Take work function of sodium as 2.0eV).

Given that me= 9.109 x 10-31kg,

mn= 1.675 x 10-27kg, and

mp= 1.672 x 10-27kg

Evaluate the moment of inertia of a thin rod with axis of rotation at the centre , if its length is 100cm and its mass is 2.3kg.

Which part of the Planck radiation formula dominates in the short wavelength range.

A system consisting of a mass of one gram fixed to a spring which is stretched by 1 cm. by a force of 10000 dynes, the particle being constrained to move only along the x axis. What will be the zero-point energy?

A cyclist rides 3 km west and then turns around and rides 2 km east.

(a) Draw the FBD for this motion (Assume east to be positive and west to be

negative).

(b) What is her displacement?

(c) What distance does she ride?

(d) What is the magnitude of her displacement?

ψ=squar 2/L sin (nPie x/2) find the value of x

The quantum numbers of two electrons in a two-valance electron atom are:

n1=6, l1=1, s1=1/2 and

n2=5, l2=1, s2=1/2.

Assuming L-S coupling, find possible spectroscopic terms. Show them in an energy level diagram.

For hydrogen, an electron is in 2p state. Obtain the magnitude of orbital angular momentum and possible

z-components of orbital angular momentum 𝐿⃗ . What would be the possible values of total angular

momentums (𝐽 ) and associated magnetic moments 𝜇𝐽

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