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Foundations of Quantum Mechanics
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1
Question
What are the three phenomena that classical mechanics failed to explain, leading to the development of quantum mechanics?
Page 2
Answer
1. Stability of an atom 2. Spectral series of Hydrogen atom 3. Black body radiation
2
Question
Who presented the paper 'On the theory of Energy distribution law of the Normal Spectrum' at a meeting of the German Physical Society, marking the start of quantum mechanics?
Page 2
Answer
Max Planck
3
Question
How is quantum mechanics related to classical physics?
Page 3
Answer
Quantum mechanics is a generalization of classical physics that includes classical laws as special cases.
4
Question
What does quantum physics extend the range of classical physics to?
Page 3
Answer
The region of small dimensions.
5
Question
Just as the velocity of light signifies the universal constant, what characterizes quantum physics?
Page 3
Answer
Planck's constant.
6
Question
What is the value of Planck's constant in erg·sec?
Page 3
Answer
\( h = 6.65 \times 10^{-27} \) erg·sec
7
Question
What is the value of Planck's constant in Joule·sec?
Page 3
Answer
\( h = 6.625 \times 10^{-34} \) Joule·sec
8
Question
What are the four phenomena that quantum mechanics successfully explains?
Page 4
Answer
1. Photoelectric effect 2. Black body radiation 3. Compton effect 4. Emission of line spectra
9
Question
In what year was the modern approach of quantum mechanics highly successful in explaining the behavior of atoms, molecules, and nuclei?
Page 4
Answer
1925
10
Question
What is the photoelectric effect?
Page 5
Answer
It is the phenomenon of ejection of electrons from the surface of a metal when light of suitable frequency falls on it. These emitted electrons are called photoelectrons.
11
Question
In the photoelectric effect setup, what components are typically involved?
Page 5
Answer
Evacuated tube, metal surface (emitter), collecting plate, voltage source V, ammeter A.
12
Question
What is the first experimental finding of the photoelectric effect?
Page 6
Answer
There is no time lag between the arrival of light at the metal surface and the emission of electrons.
13
Question
What happens to the photocurrent when the voltage is increased to a certain value \( V_s \) in the photoelectric effect?
Page 6
Answer
The photocurrent reduces to zero.
14
Question
In the photoelectric effect, how does increasing the intensity of light affect the number of photoelectrons and their energy?
Page 6
Answer
The number of photoelectrons increases in intensity, but the energy of each electron remains the same.
15
Question
What is the fourth experimental finding of the photoelectric effect regarding frequencies below a critical value?
Page 7
Answer
At frequencies below a certain critical frequency (characteristic of each particular metal), no electron is emitted.
16
Question
What is the threshold frequency in the photoelectric effect?
Page 8
Answer
It is a certain minimum frequency below which photoelectric emission does not take place, whatever may be the intensity of the incident radiation.
17
Question
How does the maximum kinetic energy of photoelectrons depend on the frequency of incident light?
Page 8
Answer
For a given frequency greater than the threshold frequency, the maximum velocity of electrons increases with increase in frequency of the incident light.
18
Question
Why is the emission of photoelectrons independent of the intensity of light above threshold frequency?
Page 8
Answer
Photoelectric emission is less than 10^{-9} sec even when the intensity of incident light is low as 10^{-10} W/m².
19
Question
According to Einstein's photoelectric explanation, how is the energy of an incident photon utilized?
Page 9
Answer
1. A part of energy is used to free the electron from the atom known as photoelectric work function \( W_0 \). 2. Other part is provided as kinetic energy \( \frac{1}{2}mv^2 \) to the emitted electron.
20
Question
What is Einstein's photoelectric equation?
Page 9
Answer
\( hv = W_0 + \frac{1}{2}mv^2 \)
21
Question
What is the photoelectric work function \( W_0 \)?
Page 9
Answer
It is the minimum energy required to free the electron from the atom.
22
Question
Express Einstein's photoelectric equation in terms of maximum kinetic energy \( KE_{max} \).
Page 10
Answer
\( hv = W_0 + KE_{max} \)
23
Question
What is the condition for no photoelectric effect to occur?
Page 10
Answer
If \( v < v_0 \), no photoelectric effect.
24
Question
Express the work function \( W_0 \) in terms of threshold frequency \( v_0 \).
Page 10
Answer
\( W_0 = hv_0 = \frac{hc}{\lambda_0} \)
25
Question
What is the expression for the threshold wavelength \( \lambda_0 \) in angstroms when \( W_0 \) is in eV?
Page 10
Answer
\( \lambda_0 = \frac{12400}{W_0 (eV)} \) Å
26
Question
If \( V_0 \) is the stopping potential, what is the maximum kinetic energy of photoelectrons?
Page 11
Answer
\( KE_{max} = (v - v_0) h \) \( eV_0 = hv - hv_0 \) \( V_0 = \frac{h}{e} (v - v_0) \)
27
Question
What is the form of the graph between stopping potential \( V_0 \) and frequency \( v \)?
Page 11
Answer
It is in the form of \( y = mx + c \). The graph with \( V_0 \) on y-axis and \( v \) on x-axis will be a straight line with slope \( h/e \).
28
Question
What did Einstein postulate to explain detailed results of the photoelectric experiment?
Page 12
Answer
The existence of a particle called a photon.
29
Question
What is the energy of a photon?
Page 12
Answer
\( E_p = hv = \frac{hc}{\lambda} \)
30
Question
What are the properties of a photon?
Page 12
Answer
Photon has zero rest mass, travels at speed of light. Explains 'instantaneous' emission of electrons in photoelectric effect, frequency dependence.