Planck's Quantum Hypothesis

Q.

How to calculate the energy of a photon?

Q. A wavelength of $450$ $nm$ corresponds to :
$(1$ $nm$ = ${10}^{-9}m)$

1. Frequency$\left(\nu \right)$ $=6.6\times {10}^{14}Hz$
2. Wave number$\left(\tilde{\nu }\right)$ $=2.2\times {10}^6{m}^{-1}$
3. None of the above
4. Both (a) and (b)

Q. What is a packet of energy called?

1. Electron
2. Photon
3. Positron
4. Proton

Q. A $100W$ power source emits green light having a wavelength of $5000\stackrel{\circ }{A}$. How many photons are emitted per minute by the source?

1. $1.5\times {10}^{20}$
2. $3.5\times {10}^{22}$
3. $1.5\times {10}^{22}$
4. $3.5\times {10}^{20}$

Q. What is the energy in eV required to excite the electron from n = 1 to n = 2 energy level in a hydrogen atom? (n = principal quantum number)

1. 13.6
2. 3.4
3. 17
4. 10.2

Q. Calculate the number of photons emitted by $100\text{W}$ yellow lamp in $1\text{s}$. If the wavelength of yellow light is $560\text{nm}$ and assuming $100\%$ efficiency.

1. $8.67\times {10}^{20}$
2. $5.48\times {10}^{12}$
3. $4.26\times {10}^{20}$
4. $2.82\times {10}^{20}$

Q. Calculate the wavelength of a photon having an energy of 2 eV

1. $6.20\times {10}^3$ nm
2. $6.21\times {10}^3\stackrel{\circ }{A}$
3. $4.41\times {10}^3$ nm
4. $4.41\times {10}^3\stackrel{\circ }{A}$

Q. Calculate the energy in kilocalorie per mole of photons of an electromagnetic radiation having a wavelength of $6600\stackrel{\circ }{A}$.

1. 56.87 kcal/mol
2. 43.32 kcal/mol
3. 23.68 kcal/mol
4. 65.46 kcal/mol

Q.

Which of the following is not a characteristic of Planck's quantum theory of radiation?

1. Energy is not absorbed or emitted in whole number multiples of quantum.

2. Radiation is associated with energy

3. Radiation is associated with energy emitted or absorbed in the form of small packets called quanta.

4. The magnitude of energy associated with quantum is proportional to frequency.

Q. Photons of minimum energy 496 kJ/mol are needed to ionize sodium atoms. Calculate the lowest frequecy of light that will ionize a sodium atom.

1. $1.24\times {10}^{14}{\text{s}}^{-1}$
2. $1.24\times {10}^{15}{\text{s}}^{-1}$
3. $2.48\times {10}^{15}{\text{s}}^{-1}$
4. $2.48\times {10}^{14}{\text{s}}^{-1}$

Q. Calculate the wavelength of a photon having an energy of 3 eV. Take $h=6.6\times {10}^{-34}Js$

1. $4.125\times {10}^3\stackrel{\circ }{A}$
2. $4.125\times {10}^4\stackrel{\circ }{A}$
3. $5.125\times {10}^3\stackrel{\circ }{A}$
4. $7.125\times {10}^3\stackrel{\circ }{A}$

Q. A dye emits $50\%$ of the absorbed energy as fluorescence. If the number of quanta absorbed and the emitted out are in ratio $1:4$. Find the wavelength of emitted radiation if the absorbed radiation has a wavelength of $x\stackrel{o}{\text{A}}$.

1. $x\stackrel{o}{\text{A}}$
2. $0.5x\stackrel{o}{\text{A}}$
3. $4x\stackrel{o}{\text{A}}$
4. $8x\stackrel{o}{\text{A}}$

Q. Wavelengths of different radiations are given below:
$\lambda \left(A\right)=400\text{nm}\lambda \left(B\right)=400\mu \text{m}$
$\lambda \left(C\right)=40\text{nm}\lambda \left(D\right)=40\stackrel{\circ }{A}$
Arrange these radiations in the increasing order of their energies:

1. $A<B<C<D$
2. $C<B<D<A$
3. $B<A<C<D$
4. $C<D<A<B$

Q. A green bulb and a red bulb are emitting the radiations with equal power. The correct relation between numbers of photons emitted by the bulbs per second is:
number of photons of green bulb = $n_g$ and $\lambda =570nm$
number of photons of red bulb = $n_r$ and $\lambda =700nm$

1. $n_g=n_r$
2. $n_g<n_r$
3. $n_g>n_r$
4. Unpredictable

Q. Calculate the number of photons emitted by $100\text{W}$ yellow lamp in $1\text{s}$. If the wavelength of yellow light is $560\text{nm}$ and assuming $100\%$ efficiency.

1. $8.67\times {10}^{20}$
2. $5.48\times {10}^{12}$
3. $4.26\times {10}^{20}$
4. $2.82\times {10}^{20}$

Q. A certain laser transition emits $6.37\times {10}^{15}{\text{quanta sec}}^{-1}{\text{m}}^{-2}$. Calculate the power output in ${\text{J sec}}^{-1}{\text{m}}^{-2}$.
Given: $\lambda =632.8\text{nm}$

1. $2.5\times {10}^{-3}{\text{J sec}}^{-1}{\text{m}}^{-2}$
2. $2.0\times {10}^{-3}{\text{J sec}}^{-1}{\text{m}}^{-2}$
3. $1.6\times {10}^{-3}{\text{J sec}}^{-1}{\text{m}}^{-2}$
4. $2.3\times {10}^{-3}{\text{J sec}}^{-1}{\text{m}}^{-2}$

Q. Calculate the wavelength of the radiation that would cause photo dissociation of oxygen molecule if the $O=O$ bond energy is $498\text{kJ/mol}$ .
(take Avogadro's number to be $6\times {10}^{23}$, and Planck's constant (h) = $6.6\times {10}^{-34}\text{J s}$)

1. $8.72\times {10}^{-7}\text{m}$
2. $9.25\times {10}^{-10}\text{m}$
3. $2.38\times {10}^{-7}\text{m}$
4. $4.95\times {10}^{-7}\text{m}$

Q. Which of the following relations do not represent the correct relation of the potential energy of an electron in the $n^{th}$ shell of an hydrogen atom?

1. $P.E.\left(n\right)=2\times \text{total energy of}{n}^{th}\text{shell}$
2. $\text{Total Energy (n) = -K.E. (where K.E. is kinetic energy of electron in}{n}^{th}\text{shell})$
3. $P.E.\left(n\right)=-\frac{K{e}^2}{r_n^2}\text{(Where K is Coulomb constant and}{r}_n\text{= radius of}{n}^{th}\text{shell)}$
4. $P.E.\left(n\right)=\frac{-27.2}{n^2}eV$

Q. Sun glasses have small amount of $AgCl$ incorporated in the lenses. When light of appropriate wavelength is exposed it turns to gray colour to reduce the glare following the reactions:
$AgCl\stackrel{hv}{\to }Ag\left(\text{Gray}\right)+\frac{1}{2}C{l}_2$

If the heat of reaction for the decomposition of $AgCl$ is $248{\text{kJ mol}}^{-1}$. Find the wavelength needed to induce the desired process?

1. $4.83\times {10}^{-7}\text{m}$
2. $9.66\times {10}^{-7}\text{m}$
3. $2.41\times {10}^{-7}\text{m}$
4. $4.83\times {10}^{-6}\text{m}$

Q. Sun glasses have small amount of $AgCl$ incorporated in the lenses. When light of appropriate wavelength is exposed it turns to gray colour to reduce the glare following the reactions:
$AgCl\stackrel{hv}{\to }Ag\left(\text{Gray}\right)+\frac{1}{2}C{l}_2$

If the heat of reaction for the decomposition of $AgCl$ is $248{\text{kJ mol}}^{-1}$. Find the wavelength needed to induce the desired process?

1. $4.83\times {10}^{-7}\text{m}$
2. $9.66\times {10}^{-7}\text{m}$
3. $2.41\times {10}^{-7}\text{m}$
4. $4.83\times {10}^{-6}\text{m}$

Q. Wavelength of photon having energy 2 $eV$:

1. $6.20\times {10}^4\stackrel{o}{A}$
2. $6.20\times {10}^3\stackrel{o}{A}$
3. $6.20\times {10}^2\stackrel{o}{A}$
4. $6.20\times {10}^5\stackrel{o}{A}$

Q. A dye absorbs a photon of wavelength λ and re-emits the same energy into two photons of wavelength ${\lambda }_1$ and ${\lambda }_2$ respectively. The wavelength λ is related with ${\lambda }_1$ and ${\lambda }_2$ as:

1. $\lambda =\frac{({\lambda }_1+{\lambda }_2)}{\left({\lambda }_1{\lambda }_2\right)}$
2. $\lambda =\frac{\left({\lambda }_1{\lambda }_2\right)}{({\lambda }_1+{\lambda }_2)}$
3. $\lambda =\frac{({\lambda }_1^2+{\lambda }_2^2)}{\left({\lambda }_1{\lambda }_2\right)}$
4. $\lambda =\frac{\left({\lambda }_1^2{\lambda }_2^2\right)}{({\lambda }_1+{\lambda }_2)}$

Q.

The dissociation energy of $H_2$ is 430.53 kJ $mo{l}^{-1}$. If hydrogen is dissociated by illumination with radiation of wavelength 253.7 nm, the fraction of the radiant energy which will be converted into kinetic energy is given by

1. 1.22%

2. 8.76%

3. 2.22%

4. 100%

Q. A $100W$ power source emits green light having a wavelength of $5000\stackrel{\circ }{A}$. How many photons are emitted per minute by the source?

1. $1.5\times {10}^{20}$
2. $3.5\times {10}^{22}$
3. $1.5\times {10}^{22}$
4. $3.5\times {10}^{20}$

Q. A sodium street light gives off yellow light that has a wavelength of 600 nm. Then
( h = $6.6\times {10}^{-34}$J.s)

1. Frequency of this light is $7\times {10}^{14}{s}^{-1}$
2. Frequency of this light is $5\times {10}^{14}{s}^{-1}$
3. Wavenumber of the light is $3\times {10}^6{m}^{-1}$
4. Energy of the photon is 5 eV

Q. A certain source of radiation emits $8\times {10}^{15}{\text{quanta sec}}^{-1}$. Calculate the power output in ${\text{J sec}}^{-1}$.
Given: $\lambda =840\text{nm}$

1. $2.55\times {10}^{-3}{\text{J sec}}^{-1}$
2. $1.89\times {10}^{-3}{\text{J sec}}^{-1}$
3. $3.28\times {10}^{-3}{\text{J sec}}^{-1}$
4. $1.32\times {10}^{-3}{\text{J sec}}^{-1}$

Q. The dissociation energy of $H_2$ is 430.53 kJ/mol. If $H_2$ is exposed to a radiation of wavelength of 253.7 nm, what percent of radiant energy will be converted into kinetic energy?

1. 5.69%
2. 13.59%
3. 8.46%
4. 18.56%

Q. A near ultraviolet photon of 300 nm is absorbed by a gas and then remitted as two photons. One photon is red with wavelength of 760 nm. What would be the wave number of the second photon?

1. $2\times {10}^6{m}^{-1}$
2. $2\times {10}^4{m}^{-1}$
3. $2\times {10}^5{m}^{-1}$
4. $2\times {10}^{11}{m}^{-1}$

Q. A 100 watts bulb has an efficiency of 80%. The wavelength of the radiation emitted is 595.80 nm. Which of the following statement(s) is/are true?

1. Number of photons emitted per second is $24\times {10}^{19}$
2. 80 J of energy is emitted as light.
3. If the efficiency is 50%, then the number of photons emitted is $15\times {10}^{19}$
4. All of the above

Q. A bulb emits light of wavelength $\left(\lambda \right)=4500\stackrel{o}{A}$ . The bulb is rated as $150watt$ and $8\%$ of its energy is emitted as light. If number of photons emitted is $x\times {10}^{19}$, then the value of $x$ is:
(Take $\text{planck's constant}h=6\times {10}^{-34}Js\text{and speed of light}c=3\times {10}^{8}m{s}^{-1}$)