1. What is the physical significance of wave function ?

Ans:

a. The probability of finding a particle in space, at any given instant of time is characterized by a function Ψ(x, y, z) called wave-function.
b. It relates the particle and the wave statistically.
c. It gives the information about the particle behavior.
d. It is a complex quantity.
e. |Ψ 2| Represents the probability density of the particle, which is real and positive.

2.What is Compton wavelength? Give its value.

Ans:

The shift in wavelength corresponding to the scattering angle of 900 is called Compton wavelength.

3.What do you understand by the term wave function?

Ans:

Wave function Ψ is a variable quantity that is associated with a moving particle at any position (x, y, z) and at any time‘t’. It relates the probability of finding the particle at that point and at that time.

4. Define Eigen value and Eigen function.

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Eigen value is defined as energy of the particle and is denoted by the letter En. Eigen function is defined as the wave function of the particle and is denoted by the letter.

5.What is meant by degenerate and non-degenerate state? Give examples.

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Degenerate state: for various combinations of quantum numbers if we get same Eigen value (Energy levels) but different Eigen functions, then it is called degenerate state.
Non- degenerate state: for various combinations of quantum numbers if we get same Eigen values (Energy levels) and same Eigen functions, then it is called.

6. How Is A Particle Composed Of Many Waves?

Ans:

It isn’t. De Broglie thought he could make such a thing with his matter waves to explain the wavelike properties of particles. But it didn’t work, because of the probabilistic nature of the interference. We have learned from Max Born and others that we have to represent a particle by a probability function. This function, not the particle itself, we represent sometimes by the wave packet sum.

7. Differentiate between Optical Microscope and electron microscope.

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8. Explain what is Wave-Particle duality?

Ans:

When matter and light exhibits properties of both waves and particles, it is referred asWave-Particle duality. For instance, Light can behave like wave when it shines throughnarrow slits while, when exposed to some metal surface it will spray electrons acting as aparticle. So under different conditions it will act.

9. Explain what is Uncertainty principle?

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Uncertainty principle tells that the momentum and position of a particle cannot be measuredprecisely.

10. Why ”quantum physics” is named as it is?

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In 1905 Albert Einstein explained the photoelectric phenomena by assuming that light can be absorbed in certain “packets”, only. He suggested that light has an elementary “quanta” the photon, as it was then called. This contributed to the birth of a new physics in an important way.

11. Describe Planck’s three experimental observations that explain the photoelectric effect.

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“When a specific frequency of light shines on a clean metal surface, electrons are ejected from the metal.” Experiment results show that:
1) The number of electrons ejected is proportional to the light intensity.
2) The frequency of the ejected light is proportional to the kinetic energy of the ejected electrons.
3) If the frequency of the light is less than a certain value, known as the threshold frequency, no electrons can be ejected ( nu_O ).

12. State Heisenberg’s uncertainty principle. Give its mathematical expression.

Ans:

Heisenberg’s uncertainty principle states that the position and momentum of microscopic moving particles cannot be determined with accuracy or certainty at the same time.
Its mathematical expression is-
Δx × ΔP ≥ h/4π
Δx = uncertainty in the position
ΔP = uncertainty in the omentum
h = Planck’s constant

13. An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momentum,
(b) the energy of the photon, and
(c) the kinetic energy of the electron.

Ans:

(a) According to De Broglie’s hypothesis,
p = h/λ
p=6.62×10^-341×10^-9=6.62×10^-25kg−m/s.
The value will remain the same irrespective of electron or photon.
(b) λ = 1nm
E = hc/λe = 1243.1 eV = 1.243 KeV
(c) Momentum, p = h/λ = 6.63 × 10^-25 kg-m/s
K.E of electron is P2/2m =2.415 × 10^-19 J =1.51 eV.

14. Find the uncertainty in the position of an electron when the mass of an electron is 9.1×10^-28g and the uncertainty in velocity is equal to 2×10^-3 cm/sec.

Ans:

Δx × ΔP ≥ h/4π
ΔP =mΔV = 9.1 × 10^-28 gm × 2 × 10^-3 cm/sec
= 1.82 × 10^-30 g-cm/sec
= 1.82 × 10^-35 kg-m/sec
Therefore, Δx = h/4πΔP = 2.9 m = 2.9 × 10² cm.

15. What Is This Wave Function ψ?

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It is the function which gives all the information that there is about a quantum system. A quantum system can be one or many particles.

16. What Is A Wave Packet?

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It is a group of waves, each of different wavelength, added together in a way to produce one wave which only shows up in some finite region of space and time. We have then produced a localized wave packet. If we calculate ψ for this wave packet function, it will be zero everywhere expect one small region of space and time.

17. Explain what is Wave-Particle duality?

Ans:

When matter and light exhibits properties of both waves and particles, it is referred as Wave-Particle duality. For instance, Light can behave like wave when it shines through narrow slits while, when exposed to some metal surface it will spray electrons acting as a particle. So under different conditions it will act.