91Ó°ÊÓ

Calculate the de Broglie wavelength of (a) a golf ball of mass \(50 \mathrm{g}\) moving at \(20 \mathrm{m} / \mathrm{s}\) and (b) an electron with kinetic energy of \(10 \mathrm{eV}.\)

The threshold of sensitivity of the human eye is about 100 photons per second. The eye is most sensitive at a wavelength of around \(550 nm\). For this wavelength, determine the threshold in watts of power.

What is the energy, in electron volts, of light photons at the ends of the visible spectrum, that is, at wavelengths of 380 and \(770 \mathrm{nm} ?\)

Determine the wavelength and momentum of a photon whose energy equals the rest-mass energy of an electron.

Show that the rest-mass energy of an electron is 0.511 \(\mathrm{MeV}.\)

Show that the relativistic momentum of an electron, accelerated through a potential difference of 1 million volts, can be conveniently expressed as \(1.422 \mathrm{MeV} / \mathrm{c}\), where \(c\) is the speed of light.

Show that the wavelength of a photon, measured in angstroms, can be found from its energy, measured in electron volts, by the convenient relation $$\lambda(\dot{\mathrm{A}})=\frac{12,400}{E(\mathrm{eV})}.$$

Show that the relativistic kinetic energy, $$E_{K}=m c^{2}(\gamma-1)$$ reduces to the classical expression \(\frac{1}{2} m v^{2},\) when \(v \ll c.\)

A proton is accelerated to a kinetic energy of 2 billion electron volts \((2 \mathrm{GeV}) .\) Find \((\mathrm{a})\) its momentum, \((\mathrm{b})\) its de Broglie wavelength, and (c) the wavelength of a photon with the same total energy.

Solar radiation is incident at the earth's surface at an average of \(1000 \mathrm{W} / \mathrm{m}^{2}\) on a surface normal to the rays. For a mean wavelength of \(550 \mathrm{nm}\), calculate the number of photons falling on \(1 \mathrm{cm}^{2}\) of the surface each second.