Planck's Quantum Hypothesis

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. In hydrogen like species energy depends on?? And in multi electron species energy depends on??

Q. Calculate the wavelength of the radiation which would cause the photo-dissociation of chlorine molecule if the Cl-Cl bond energy is 243 kJ/mol.

1. $493nm$
2. $4900\mu m$
3. $4900nm$
4. $493m$

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. Calculate the energy associated with photon of light having a wavelength 6000 $\stackrel{o}{A}$. [h= $6.626\times {10}^{-27}ergs$]

1. $3.313\times {10}^{-11}erg$
2. $3.313\times {10}^{-12}erg$
3. $3.313\times {10}^{-13}erg$
4. $3.313\times {10}^{-10}erg$

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. A $100\text{watt}$ bulb emits monochromatic light of wavelength $396\text{nm}$. Calculate the number of photons emitted per second by the bulb.

1. $3.75\times {10}^{20}$
2. $4.0\times {10}^{20}$
3. $2.0\times {10}^{20}$
4. $37.5\times {10}^{20}$

Q. Calculate the wavelength of a light wave whose time period is $3\times {10}^{-10}s$.

1. $3.3\times {10}^{9}cm$
2. $3.3\times {10}^{-9}m$
3. $9\times {10}^{-2}m$
4. $9\times {10}^{7}cm$

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. The velocity of an electron in the first Bohr orbit of a hydrogen atom is equal to the velocity of the electron in the $n^{th}$ Bohr orbit of $B{e}^{3+}$ atom. Find the value of n.

1. 8
2. 4
3. 16
4. 2

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 $\text{planck's constant}h=6\times {10}^{-34}Js\text{and speed of light}c=3\times {10}^{8}m{s}^{-1}$)

Q. Calculate the energy associated with photon of light having a wavelength 6000 $\stackrel{o}{A}$. [h= $6.626\times {10}^{-27}ergs$]

1. $3.313\times {10}^{-11}erg$
2. $3.313\times {10}^{-12}erg$
3. $3.313\times {10}^{-13}erg$
4. $3.313\times {10}^{-10}erg$

Q. A uniform thin metallic rod of length l = 8 m, is hinged at point A (at a distance $\frac{l}{4}$ from one end of the rod). If the rod is rotated with angular speed 2 rad/s about hinge in a uniform magnetic field of magnitude 4 T perpendicular to the plane of rotation. The induced emf between two ends of the rod will be

लम्बाई l = 8 m की एक समरूप पतली धात्विक छड, बिंदु A (छड़ के एक सिरे से $\frac{l}{4}$ दूरी पर) पर कीलकित है। यदि छड़ को घूर्णन तल के लम्बवत् 4 T परिमाण वाले एकसमान चुम्बकीय क्षेत्र में कीलक के सापेक्ष कोणीय चाल 2 rad/s से घुमाया जाता है। तब छड़ के दोनों सिरों के मध्य प्रेरित वि.वा.ब. होगा

1. 98 V
2. 144 V
3. 128 V
4. 61 V

Q. A bulb emits light having $\lambda =5500\stackrel{\circ }{A}$. The bulb is rated as $100$ watt and 15% of the energy is emitted as light. How many photons are emitted by the bulb per second?

1. $4.15\times {10}^{11}$
2. $2.68\times {10}^{11}$
3. $4.15\times {10}^{19}$
4. $2.68\times {10}^{19}$

Q. Calculate the energy associated with photon of light having a wavelength 6000 $\stackrel{o}{A}$. [h= $6.626\times {10}^{-27}ergs$]

1. $3.313\times {10}^{-13}erg$
2. $3.313\times {10}^{-11}erg$
3. $3.313\times {10}^{-10}erg$
4. $3.313\times {10}^{-12}erg$

Q. what are the assumptions of plancks quantum theory

Q. The value of Planck's constant is $6.63\times {10}^{-34}Js.$ The velocity of light is $3\times {10}^{8}m/s.$ If the wavenumber of a quantum of light is $2.5\times {10}^7{m}^{-1}$, calculate its frequency.

1. $7.5\times {10}^{15}{s}^{-1}$
2. $3\times {10}^{15}{s}^{-1}$
3. $11\times {10}^{15}{s}^{-1}$
4. $5\times {10}^{15}{s}^{-1}$

Q.

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

1. (a)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 continuously but in the form of small packets called quanta.

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

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. 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.

A copper disc of radius$0.1m$ is rotated about its center with $20rev/s$ in a uniform magnetic field of $0.1T$ with its plane perpendicular to the field. The emf induced across the radius of the disc is

1. $\pi /20V$

2. $10/\pi V$

3. $20\pi mV$

4. $10\pi mV$

Q.

The wavelength range of the visible spectrum extends from violet (400 nm) to red (750 nm). Express these wavelength in frequencies (Hz). $(1nm={10}^{-9}m)$.

1. $4\times {10}^{14}to7.5\times {10}^{14}Hz$

2. $8\times {10}^{14}to16\times {10}^{14}Hz$

3. $7\times {10}^{14}to16\times {10}^{14}Hz$

4. $7.5\times {10}^{14}to16\times {10}^{14}Hz$

Q. During photosynthesis, chlorophyll absorbs light of wavelength $440\text{nm}$ and emits light of wavelength $670\text{nm}$. What is the energy (in kJ/mol) available for photosynthesis from the absorption-emission of a mole of photons?

1. 85.20 $kJmo{l}^{-1}$
2. 105.20 $kJmo{l}^{-1}$
3. 98.40 $kJmo{l}^{-1}$
4. 93.30 $kJmo{l}^{-1}$

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. The equation $E=hv$ indicates that:

1. Photons are waves
2. Photons are stream of particles
3. Photons have both particle and wave nature
4. No such inference can be drawn from the given equation

Q. Find the number of quanta of radiations of frequency $5.03\times {10}^{13}{\text{s}}^{-1}$ that must be absorbed in order to melt 5 g of ice. The energy required to melt 1 g of ice is 333 J.

1. $5.38\times {10}^{23}$
2. $6.52\times {10}^{22}$
3. $5.00\times {10}^{22}$
4. $6.37\times {10}^{22}$

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.

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.

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 proton captures a free electron whose K.E. is zero & forms a hydrogen atom of lowest energy-level (n = 1). If a photon is emitted in this process, what will be the wavelength (in $\stackrel{\circ }{A}$) of radiation? (report the answer to the nearest integer) (Ionisation potential of hydrogen =13.6 volt, $e=1.6\times {10}^{-19}J,h=6.6\times {10}^{-34}Js,c=3.0\times {10}^{8}m/s$)