Photon Theory of Light

If the energy of a photon is given as, $\text{E}=3.03\times {10}^{-19} \mathrm{J}$, then, the wavelength $\mathrm{(\lambda )}$ of the photon is

Find the relation between the $\mathrm{eV}$ and $\mathrm{joule}$ using the definition of one electron volt.

Find the change in potential energy of an alpha particle in the units of $\mathrm{eV}$ , when it moves between two points with a potential difference of $1000 \mathrm{V}$.

The electron volt can be used as a unit to express:

Electron volt is a unit of potential difference.

The photoelectric cut-off voltage in a certain experiment is $1.5 \mathrm{V}$. What is the maximum kinetic energy of photoelectrons emitted?

What is the de Broglie wavelength in $\mathrm{nm}$ associated with an electron, accelerated through a potential difference of $100$ volts?

A $100 \mathrm{W}$ sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is $589 \mathrm{nm}$. At what rate are the photons from the lamp associated with the sodium light?

A $100\text{W}$ sodium lamp radiates energy uniformly in all directions. The wavelength of the sodium light is $589\text{ nm}$. What is the energy per photon in $\left(\mathrm{eV}\right)$ associated with the sodium light? [ $h= 6.63{\times 10}^{-34} \mathrm{J} s$ ]

The energy flux of sunlight reaching the surface of the earth is $1.388 \times {10}^3 \mathrm{W} {\mathrm{m}}^{-2}$. The number of photons (nearly) per square meter are incident on the earth per second is (Assume that the photons in the sunlight have an average wavelength of $550 \mathrm{nm}$).

For light of wavelength $5000 A°$, photon energy is nearly $2.5 eV$. For X-Ray of wavelength $1 A°$, the photon energy will be close to

The total momentum delivered (for complete absorption) of energy flux of $30 \mathrm{W}/{\mathrm{cm}}^2$ falling on a non-reflecting surface of surface area $40 {\mathrm{cm}}^2$ at normal incidence, during $30 \mathrm{minutes}$ is found be $\mathrm{N}\times {10}^{-4} \mathrm{SI}$ units. Calculate the value of $\mathrm{N}$.

A $2 \mathrm{cm}$ thick parallel beam of light of frequency $1.6\times {10}^{15} \mathrm{Hz}$ and power $6.62$ watt is directed on emitter as shown in figure. Neglect any loss of energy during reflection and refractions. If work function of emitter is $6 \mathrm{eV}$ then the number of photons incident on emitter plate per second is $\frac{\mathrm{K}}{100}\times {10}^{18}\left( \mathrm{h}=6.62\times {10}^{-34} \mathrm{J} \mathrm{s}\right)$ find $\mathrm{K}.$

A free nucleus of mass $24$ amu, initially at rest emits $\mathrm{a}$ gamma photon. The energy of the photon is $7\mathrm{MeV}$. The kinetic energy of recoiling nucleus is approximately in $\mathrm{keV}$ is.  [Take : $1$ amu $=9.31\mathrm{MeV}$ ]

Two sources $S_1$ and $S_2$ produce ${10}^{15}$ photons per second of wavelength $5000 Å$ and $1.02\times {10}^{15}$ photons per second of wavelength $5100 Å$, respectively. Calculate the ratio of power of $S_1$ to power of $S_2$.

A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $\Omega$ such that $\frac{4\pi \mathrm{M}\Omega }{\mathrm{h}}={10}^{24} {\mathrm{m}}^{-2}$ with $h$ as Planck's constant. $N$ photons of wave- length $\lambda =8\pi \times {10}^{-6} m$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1 \mu \mathrm{m}.$ If the value of $N$ is $\mathrm{x}\times {10}^{12},$ then the value of $x$ is

A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $\omega$ such that $\frac{4\pi M\omega }{h}={10}^{24} {\mathrm{m}}^{-2}$ with $h$ as Planck's constant. $N$ photons of wavelength $\mathrm{\lambda }=8\mathrm{\pi }\times {10}^{-6} \mathrm{m}$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1 \mu \mathrm{m}$. If the value of $N$ is $x\times {10}^{12}$. Then the value of $x$ is [Consider the spring as massless]

The energy $E$ and momentum $p$ of photon is given by $E=h\nu$ and $p=\frac{h}{\lambda },$ the velocity of photon will be-

A $1.5 \mathrm{kW}$ (kilo-watt) laser beam of wavelength $6400 \mathrm{A}$ is used to levitate a thin aluminium disk of same area as the cross-section of the beam. The laser light is reflected by the aluminium disk without any absorption. The mass of the foil is close to,

An electron-positron pair (rest mass of each particle is $0.51\mathrm{MeV}$ ) is produced by a $\gamma$-ray photon of energy $2.42\mathrm{MeV}$. The K.E. imparted to each of the charged particles shall be-