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Historical introduction to quantum mechanics - Set no. 3
1) Suppose that a 60 W light bulb radiates primarily at a wavelength 1000 nm. What is the
number of photons emitted per second ?
2) What is the number of photons emitted per second by the Sun? Lets assume that the star
radiates electromagnetic waves with λ = 550 nm and its power equals to 3.9 · 1026 W.
3) What is the momentum of a photon which energy equals to the energy of a free electron?
What is the wavelength and frequency corresponding to such a radiation?
4) The wavelength of X-ray radiation equals to 35 pm. What is the corresponding frequency?
Please calculate the energy of the photon and its momentum.
5) In which range of the electromagnetic radiation the momentum of photons takes the
largest value: ultraviolet, X-ray radiation, radio waves, infrared?
6) What is the flux of photons (unit: number/m2) in the case of homogeneous beam with
wavelength 500 nm and intensity 2000 W/m2?
7) The smallest energy required to emit electron from metallic sodium source equals to
2.28 eV. The question is if the photoelectric effect will take place when red light (λ = 680 nm)
falls on sodium? What is the boundary wavelength? Which colour corresponds to the
boundary wavelength?
8) The light falling on sodium source causes photoelectric effect. The stopping potential
equals to 5 eV and the work function W = 2.2 eV. What is the wavelength of falling
electromagnetic radiation?
9) In the experiment with metallic sodium source the stopping potential for photoelectric
effect was equal to: 1.85 eV in the case of λ1 = 300 nm and 0.82 eV for λ2 = 400 nm. Taking
into account these data, please calculate the value of Planck’s constant, work function and
the boundary wavelength for sodium.
10) Please derive the following formula for the kinetic energy of the photon which scatters
on a free electron (Compton effect):
Eγ =
Eγ mc 2
Eγ (1 − cos θ ) + mc 2
11) X-ray electromagnetic radiation with wavelength λ = 22 pm scatters on a graphite target.
The scattered radiation is observed at an angle of 85o. What is the shift of wavelength?
Calculate the percentage of the initial photon energy which is transferred to the electron
(fractional energy loss).
12) Electromagnetic radiation with wavelength 5.7 · 10-12 m scatters in the Compton effect.
What is the angle at which the wavelength 6.57 · 10-12 m can be observed?