$A$ scientist claims to have a perfect technique in which he can spontaneously convert an electron completely into energy in the laboratory without any other material required. What is the conclusion about this claim from our current understanding of physics?

  • A
    This is possible because Einstein's equation says that mass and energy are equivalent... it is just very difficult to achieve with electrons
  • B
    This is possible and it is done all the time in the high-energy physics labs.
  • C
    The scientist is almost correct... except that in converting the electron to energy, an electron's anti-particle is produced in the process as well
  • D
    This is not possible because charge conservation would be violated.

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The minimum intensity of light that can be perceived by the human eye is $10^{-10} \ W/m^2$. If the area of the pupil is $10^{-6} \ m^2$ and the wavelength of light is $560 \ nm$,approximately how many photons per second enter the eye? (Use $h = 6.6 \times 10^{-34} \ J \cdot s$ and $c = 3 \times 10^8 \ m/s$).

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If the momentum of a photon is $p$,then its frequency is ........

Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never 'count photons',even in barely detectable light.
$(a)$ The number of photons emitted per second by a Medium wave transmitter of $10\; kW$ power,emitting radiowaves of wavelength $500\; m$.
$(b)$ The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of white light that we humans can perceive $(10^{-10}\; W m^{-2})$. Take the area of the pupil to be about $0.4\; cm^2$,and the average frequency of white light to be about $6 \times 10^{14}\; Hz$.

$10^{20}$ photons of wavelength $660 \ nm$ are emitted per second from a lamp. The wattage of the lamp is (Planck's constant $h = 6.6 \times 10^{-34} \ J \cdot s$). (in $W$)

When light of wavelength $\lambda$ is incident on a photosensitive surface,photons of power $P$ are emitted. The number of photons $n$ emitted in time $t$ is: [$h$ = Planck's constant,$c$ = velocity of light in vacuum]

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