Planck's Quantum Theory

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  $8\times {10}^{16}{s}^{-1}?$

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 _______

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

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.

Electromagnetic radiation of wavelength $663 \mathrm{nm}$ is just sufficient to ionize the atom of metal $\mathrm{A}$. The ionization energy of metal $\mathrm{A}$ in $\mathrm{kJ} {\mathrm{mol}}^{-1}$ is ______.

(Rounded off to the nearest integer)

Use:

$$\begin{gathered} \mathrm{h}=6.63\times {10}^{-34}\mathrm{Js} \\ \mathrm{c}=3.00\times {10}^8 {\mathrm{ms}}^{-1} \\ {\mathrm{N}}_{\mathrm{A}}=6.02\times {10}^{23} {\mathrm{mol}}^{-1} \end{gathered}$$

What is the number of photons of light with a wavelength of $4000 \mathrm{pm}$ that provide $1 \mathrm{J}$ of energy?

When an electron present in ground state of $\mathrm{H}$-atom absorb a photon of energy $12.1 \mathrm{eV}.$ How many times its wavelength increases.

Planck's constant $6.6\times {10}^{-27} \mathrm{erg}$ second, velocity of light $=3\times {10}^{10} \mathrm{cm}/\mathrm{s}$, the energy of photon of wave-length $3000 \mathrm{\AA }$ will be :

The energy of a photon is given as $3.03\times {10}^{-19} \mathrm{J}/\mathrm{atom}$. The wavelength of the photon is :-

Planck’s constant has the units of

Which of the following transitions will have minimum wavelength?

$1$ mole of photons, each of frequency $250 {\mathrm{s}}^{-1}$ would have approximately a total energy of

$1$ mole of photons, each of frequency $250 {\mathrm{s}}^{-1}$ would have approximately a total energy of

If $a_0$ represents the Bohr radius, the de Broglie wavelength of the electron when it moves in the $3^{\mathrm{rd}}$ orbit after absorbing some definite amount of energy will be

If the ionization potential of the hydrogen atom in the ground state is$13·6 \mathrm{e} \mathrm{V}$, the longest wavelength of the radiation required to remove the electron from Bohr's first orbit will be approximately

Three energy levels and the wavelengths of the lines produced by transitions are shown in the  figure below:

Which one of the following relationship is correct?