Particle Nature of Electromagnetic Radiation

The energies  ${\mathrm{E}}_1\mathrm{and}{\mathrm{E}}_2$  of two radiations are $25 \mathrm{eV}$ and $50 \mathrm{eV}$, respectively. The relation between their wavelength i.e.,  ${\mathrm{\lambda }}_1\mathrm{and}{\mathrm{\lambda }}_2$ will be:

The value of Planck’s constant is  $6.63\times {10}^{-34}Js.$  The velocity of light is  $3.0\times {10}^{8}m{s}^{-1}.$  Which value is closest to the wavelength in meters of a quantum of light with frequency of  $8\times {10}^{16}{s}^{-1}?$

The photoelectric behaviour of $\mathrm{K}, \mathrm{Li}, \mathrm{Mg}$ and $\mathrm{Ag}$ metals is shown in the plot below. If light of wavelength $400 \mathrm{nm}$ is incident on each of these metals, which of them will emit photoelectrons? [Planck's contant $h=6.626\times {10}^{-34}\mathrm{Js}$; velocity of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}; 1\mathrm{eV}=1.6\times {10}^{-19} \mathrm{J}$]

Name the phenomenon which shows the quantum nature of electromagnetic radiation. 

The frequency of radiation emitted, when an electron falls from $n=3$ to $n=1,$ in a Hydrogen atom would be $\underline{ }$
(Given, ionisation energy of Hydrogen is$2.18\times {10}^{-18} \mathrm{J}/\mathrm{atom}$ and $h=6.625\times {10}^{-34} \mathrm{J}.\mathrm{s} )$

If the maximum kinetic energy of photoelectrons ejected from a metal surface when it is irradiated with a radiation of frequency $4\times {10}^{14}{ \mathrm{s}}^{-1}$ is $6.63\times {10}^{-20} \mathrm{J},$ then the threshold frequency of the metal is _______

The kinetic energy of the photoelectrons ejected from a metal on irradiation with light of frequency $3.8\times {10}^{16} \mathrm{Hz}$ is K. When irradiated with light of frequency $2.4\times {10}^{16} \mathrm{Hz}$, the kinetic energy of the photoelectrons becomes $\frac{\mathrm{K}}{2}$. What is the threshold frequency $\left({\mathrm{\nu }}_0\right)$ of the metal?

In case of photoelectric effect, slope of ${\mathrm{V}}_{\mathrm{0}}$ vs $\mathrm{\nu }$ curve is (where ${\mathrm{V}}_{\mathrm{0}}$ - stopping potential,$\mathrm{\nu }=$ subjected frequency)

Photoelectric effect shows:

Energy of an electron is given by $\mathrm{E}=-2· 178 \times {10}^{-18}\mathrm{J} \left(\frac{{\mathrm{Z}}^2}{{\mathrm{n}}^2}\right)$. Calculate the wavelength of light required to excite an electron in a hydrogen atom from $\mathrm{n}=1 \text{to} \mathrm{n}=2$ will be

Select the correct statement about the photoelectric experiment from the following.

The energy difference between the ground state of an atom and its excited state is $4.4\times {10}^{-\mathrm{14 }}\mathrm{J}$, calculate the wavelength of the photon required to induce the transition.

Light of wavelength $\mathrm{\lambda }$, shines on a metal surface with intensity $\mathrm{X}$, and the metal emits $\mathrm{Y}$ electrons per second of average energy $\mathrm{Z}$. What will happen to $\mathrm{Y}$ and $\mathrm{Z}$ if $\mathrm{X}$ is doubled?

The "Kangri" is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the "Kangri" is spherical and of surface area $7\times {10}^{-2} {\mathrm{m}}^2.$ It contains $300 \mathrm{g}$ of a mixture of coal, wood and leaves with calorific value of $30 \mathrm{kJ} {\mathrm{g}}^{-1}$ (and provides heat with $10\%$ efficiency). The surface temperature of the 'Kangri' is $60°\mathrm{C}$ and the room temperature is $0°\mathrm{C}.$ Then, a reasonable estimate for the duration t (in hours) that the 'kangri' heat will last is (take the 'kangri' to be a black body):

A zinc ball of radius, $R=1 \mathrm{cm}$ charged to a potential $-0.5 \mathrm{V}.$ The ball is illuminated by a monochromatic ultraviolet $\left(UV\right)$ light with a wavelength $290\mathrm{nm}.$ The photoelectric threshold for zinc is $332\mathrm{nm}.$ The potential of ball after a prolonged exposure to the $UV$ is

A certain metal has a work function of $\Phi =2\mathrm{eV}$. It is irradiated first with $1 \mathrm{W}$ of $400\mathrm{nm}$ light and later with $1 \mathrm{W}$ of $800\mathrm{nm}$ light. Among the following, the correct statement is: [Given:Planck constant $\left(\mathrm{h}\right)$$=6.626\times {10}^{-34} {\mathrm{m}}^2{\mathrm{kgs}}^{-1}$ Speed of light $\left(\mathrm{c}\right)=3\times {10}^8 {\mathrm{ms}}^{-1}$]

Ultra-violet light is shone on a zinc surface and photoelectrons are emitted. The graph shows how the stopping potential $V_{\mathrm{s}}$ varies with frequency $f.$

Planck's constant may be determined from the charge of an electron $e$ multiplied by

A certain stellar body has radius $50R_s$ and temperature $2T_s$ and is at a distance of $2\times {10}^{10} \mathrm{AU}$ from the earth. Here, $\mathrm{AU}$ refers to the earth-sun distance and $R_s$ and $T_s$ refer to the sun's radius and temperature, respectively. Take, both star and sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to