Advertisements
Advertisements
प्रश्न
Show that it is not possible for a photon to be completely absorbed by a free electron.
उत्तर
When an electron undergoes an inelastic collision with a photon, we can apply the principle of conservation of energy to this collision. So,
`pc + m_eC^2 = sqrt(p^2C^2 + m_e^2C^4) ....(1)`
Here, h = Planck's constant
c = the speed of light
me = rest mass of electron
pc = energy of the photon
Squaring on both side of equation (1),
`(pc + m_eC^2)^2 = p^2C^2 + m_e^2C^4`
`⇒ p^2C^2 + m_e^2C^4 + 2(pc)(m_eC^2) = p^2C^2 + m_e^2C^4`
`⇒ 2(pc)(m_eC^2) = 0 or pc = 0 ("as" 'm' and 'c' "are non zero")`
This gives vanishing energy of photon which is not possible.
APPEARS IN
संबंधित प्रश्न
(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 × 1011 C kg−1.
(b) Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?
Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?
Can a photon be deflected by an electric field? Or by a magnetic field?
In an experiment on photoelectric effect, a photon is incident on an electron from one direction and the photoelectron is emitted almost in the opposite direction. Does this violate the principle of conservation of momentum?
It is found that photosynthesis starts in certain plants when exposed to sunlight, but it does not start if the plants are exposed only to infrared light. Explain.
If an electron has a wavelength, does it also have a colour?
Two photons of
The equation E = pc is valid
When the intensity of a light source in increased,
(a) the number of photons emitted by the source in unit time increases
(b) the total energy of the photons emitted per unit time increases
(c) more energetic photons are emitted
(d) faster photons are emitted
When a metal plate is exposed to a monochromatic beam of light of wavelength 400 nm, a negative potential of 1.1 V is needed to stop the photo current. Find the threshold wavelength for the metal.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
In an experiment on photoelectric effect, the stopping potential is measured for monochromatic light beams corresponding to different wavelengths. The data collected are as follows:-
Wavelength (nm): 350 400 450 500 550
Stopping potential (V): 1.45 1.00 0.66 0.38 0.16
Plot the stopping potential against inverse of wavelength (1/λ) on a graph paper and find (a) Planck's constant (b) the work function of the emitter and (c) the threshold wavelength.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
The electric field associated with a light wave is given by `E = E_0 sin [(1.57 xx 10^7 "m"^-1)(x - ct)]`. Find the stopping potential when this light is used in an experiment on photoelectric effect with the emitter having work function 1.9 eV.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Define the term: threshold frequency
Define the terms "stopping potential' and 'threshold frequency' in relation to the photoelectric effect. How does one determine these physical quantities using Einstein's equation?
Do all the electrons that absorb a photon come out as photoelectrons?
Two monochromatic beams A and B of equal intensity I, hit a screen. The number of photons hitting the screen by beam A is twice that by beam B. Then what inference can you make about their frequencies?
The work function for a metal surface is 4.14 eV. The threshold wavelength for this metal surface is ______.
If photons of ultraviolet light of energy 12 eV are incident on a metal surface of work function of 4 eV, then the stopping potential (in eV) will be :
A metallic plate exposed to white light emits electrons. For which of the following colours of light, the stopping potential will be maximum?
- Assertion (A): For the radiation of a frequency greater than the threshold frequency, the photoelectric current is proportional to the intensity of the radiation.
- Reason (R): Greater the number of energy quanta available, the greater the number of electrons absorbing the energy quanta and the greater the number of electrons coming out of the metal.
