A proton has kinetic energy \mathrm{E}=100\mathrm{k}\mathrm{e}\mathrm{V} which is equal to that of a photon. The wavelength of photon is \lambda_{2} and that of proton is \lambda_{1} . The ratio of \lambda_{1}/\lambda_{2} is proportional to

For proton and photon wavelength is given as - \displaystyle \lambda_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}=\frac{\mathrm{h}}{\sqrt{2\mathrm{m}\mathrm{E}}},\ \displaystyle \lambda_{\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}=\frac{\mathrm{h}\mathrm{c}}{\mathrm{E}} .So, the answer is option (B).

An \alpha -particle and a proton are accelerated from rest by a potential difference of 100 V . After this, their de Broglie wavelengths are \lambda_{\alpha} and \lambda_{p} respectively. The ratio \dfrac{\lambda_{p}}{\lambda_{\alpha}} , to the nearest integer, is:

We have, \dfrac{1}{2}mv^{2}=eV De broglie wavelength= \lambda=\dfrac{h}{mv} \lambda = \dfrac{h}{\sqrt{2meV}} \lambda_{p}=\dfrac{h}{\sqrt{2(m)eV}} ....(1) \lambda_{\alpha}=\dfrac{h}{2(4m)2eV} ....(2)Now, \dfrac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{8} \simeq 3

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Dual Nature Of Radiation And Matter

Q: A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is : (take the proton mass, m_p = (5/3) \times 10^{-27}kg and h/e = 4.2\times 10^{-15}J.s/C; \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 m/F; 1 fm = 10^{-15}m )

Given here, q_{1} = 120 \times e q_{2} = e ( charge on proton) It is based on conservation of energy of proton. \dfrac{1}{2}mv^2 = k \dfrac{q_1q_2}{R} v = \sqrt{\dfrac{2Kq_1q_2}{mR}} Also, we know, de’broglie wavelength, \lambda =\dfrac{h}{mv} \lambda = \dfrac{h\sqrt{R}}{\sqrt{2mKq_1q_2}}\\ Thus, \lambda = \dfrac{h\sqrt{10\times10^{-15}}}{\sqrt{2\times\dfrac{5}{3}\times10^{-27}\times9\times10^9\times120\times e^2}}\\ \lambda =\dfrac{\dfrac{h}{e}\times10^{-7}}{6\times10^{-8}}\\ \lambda =\dfrac{4.2\times10^{-15}\times10^{-7}}{6\times10^{-8}}\\ \lambda =7\times10^{-15}\ m = 7\ fm \\ Option A is correct.

Q: A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3\times 10^{8}m/s . The final momentum of the object is:

Sol . (B) t=100\times 10^{-9} sec,\ P=30\times 10^{-3} Watt, C=3\times 10^{8}m/s Incident energy = Pt By debroglie wavelength, \lambda=h/p and Energy of photon is E=hc/\lambda From above two equations, E=pc Momentum p=\dfrac{Pt}{C}=\dfrac{30\times 10^{-3}\times 100\times 10^{-9}}{3\times 10^{8}}=1.0\times 10^{-17} kg ms ^{-1} So, the answer is option (B).

Q: Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II andindicate your answer by darkening appropriate bubbles in the 4 4 matrix given in the ORS.

The X-rays contains K_{\alpha}, K_{\beta} etc and these are the transitions between two atomic level . So A\rightarrow 1 Also Hydrogen spectrum has quantized energy levels i.e E_n=-\dfrac{136.6}{n^2} and it contains so many transitions between two energy levels like-Lyman, Balmer etc. So A\rightarrow 3 The photo electric effect is the emission of electron when photon incident on a metal. In beta minus decay, one neutron decay into a proton, an electron and an anti-neutrino. So, So B \rightarrow 2, 4 Mosley's law is an empirical law concerning the characteristic X-rays. So C\rightarrow 1 The Einstein's photoelectric equation is h\nu=KE_{max}-h\nu_0 . So D \rightarrow 2

Q: The speed of the particle that can take discrete values is proportional to

As given in the questionLet the no. of loops in the wave be n Let wavelength be \lambda Debroglie wavelength \lambda = \cfrac{h}{mv} ------------(1)Also n \lambda = 2 \pi a --------------(2)Substituting above v = \cfrac{nh}{2am} v \propto n So, the answer is option (D).

Q: A photon of energy 10.2 eV collides inelastically with a Hydrogen atom in ground state. After a certain time interval of few micro seconds another photon of energy 15.0 eV collides inelastically with the same hydrogen atom, then the observation made by a suitable detector is

10.2 eV photon on collision will excite H-atom to first excited state but Hydrogen atom will return to ground state before next collision. Second photon will provide ionization energy to Hydrogen atom, i.e., electron will be ejected with energy = 1.4 eV

Q: The allowed energy for the particle for a particular value of n is proportional to :

a = \cfrac{n \lambda}{2} De broglie wavelength \lambda = \cfrac{h}{mv} Subsitute p =\cfrac{nh}{2a} E = \cfrac{1}{2}mv^2= \cfrac{p^2}{2m} =\cfrac{n^2h^2}{8a^2m}

Q: Light of wavelength \displaystyle { \lambda }_{ ph } falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is \displaystyle \phi and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is \displaystyle { \lambda }_{ e } , which of the following statement(s) is(are) true?

{ \lambda }_{ e }= minimum be broglie wavelength. \dfrac { hc }{ { \lambda }_{ ph } } =\dfrac { hc }{ { \lambda }_{ e } } +\phi +eV \Rightarrow hc(\dfrac { -1 }{ { \lambda }_{ ph }^{ 2 } } d{ \lambda }_{ ph })=hc(\dfrac { -1 }{ { \lambda }_{ e }^{ 2 } } d{ \lambda }_{ e }) \Rightarrow \dfrac { d{ \lambda }_{ ph } }{ d{ \lambda }_{ e } } =\dfrac { { \lambda }_{ ph }^{ 2 } }{ { \lambda }_{ e }^{ 2 } } This denies option A, B and C. V>>\dfrac { \phi }{ e } Energy of electron, E=\dfrac { { P }^{ 2 } }{ 2m } \lambda_e =\dfrac { h }{ p } =\dfrac { h }{ \sqrt { 2mE } } =\dfrac{h}{\sqrt{2meV}} This supports option D.

Q: The graph between 1/\lambda and stopping potential (V) of three metals having work functions \phi_{1},\ \phi_{2} and \phi_{3} in an experiment of photo-electric effect is plotted as shown in the figure. Which of the following statement(s) \mathrm{i}\mathrm{s}/\mathrm{a}\mathrm{r}\mathrm{e} correct? [Here \lambda is the wavelength of the incident ray].

From photo electric effect, eV=\dfrac{hc}{\lambda}-\phi where V= stopping potential and \phi= work function. Slope , m=\tan\theta=hc/e (compare above equation with y=mx-c )If V=0 \Rightarrow \dfrac{\phi}{hc}=\dfrac{1}{\lambda} Now from given graph,for metal 1 : \dfrac{\phi_1}{hc}=0.001 for metal 2: \dfrac{\phi_2}{hc}=0.002 for metal 3: \dfrac{\phi_3}{hc}=0.004 Thus, \phi_1:\phi_2:\phi_3=1:2:4 Also, \phi=\dfrac{hc}{\lambda_0} where \lambda_0 be the threshold wavelength. For metal 2 : \lambda_{02}=1/0.002=500 nm For metal 3 : \lambda_{02}=1/0.004=250 nm As the wavelength of violet colour is around 400 nm so only metal 2 can eject violet colour light but not metal 3. Thus, options A and C is right.

Physics
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JEE Mains JEE Advanced NEET AIIMS BITSAT Easy Qs Med Qs Hard Qs

A proton has kinetic energy $E = 100 k e V$ which is equal to that of a photon. The wavelength of photon is $λ_{2}$ and that of proton is $λ_{1}$ . The ratio of $λ_{1} / λ_{2}$ is proportional to

E^{2}

E^{1 / 2}

E^{- 1}

E^{- 1 / 2}

Medium

JEE Advanced

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A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is :

(take the proton mass, $m_{p} = (5 / 3) \times 1 0^{- 27} k g$ and

$h / e = 4.2 \times 1 0^{- 15} J . s / C; \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} m / F; 1 f m = 1 0^{- 15} m$ )

7 f m

8 f m

9 f m

10 f m

Hard

JEE Advanced

View Solution

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 $m W$ and the speed of light is $3 \times 1 0^{8} m / s$ . The final momentum of the object is:

0.3 \times 1 0^{- 17} k g m s^{- 1}

1.0 \times 1 0^{- 17} k g m s^{- 1}

3.0 \times 1 0^{- 17} k g m s^{- 1}

9.0 \times 1 0^{- 17} k g m s^{- 1}

Hard

JEE Advanced

View Solution

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and
indicate your answer by darkening appropriate bubbles in the 4 4 matrix given in the ORS.

List 1Transition between two atomic energy levelsElectron emission from a materialMosleys lawChange of photon energy into kinetic energy of electrons

List 2Characteristic X-raysPhotoelectric effectHydrogen spectrum

β

-decay

Hard

JEE Advanced

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An $α$ -particle and a proton are accelerated from rest by a potential difference of $100 V$ . After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ respectively. The ratio $\frac{λ _{p}}{λ _{α}}$ , to the nearest integer, is:

Hard

JEE Advanced

View Solution

The speed of the particle that can take discrete values is proportional to

n^{- 3 / 2}

n^{- 1}

n^{1 / 2}

n

Hard

JEE Advanced

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A photon of energy $10.2 e V$ collides inelastically with a Hydrogen atom in ground state. After a certain time interval of few micro seconds another photon of energy $15.0 e V$ collides inelastically with the same hydrogen atom, then the observation made by a suitable detector is

1 photon with energy

10.2 e V

and an electron with energy

1.4 e V

2 photon with energy

10.2 e V

2 photon with energy

1.4 e V

One photon with energy

3.4 e V

and 1 electron with energy

1.4 e V

Hard

JEE Advanced

View Solution

The allowed energy for the particle for a particular value of n is proportional to :

a^{- 2}

a^{- 3 / 2}

a^{- 1}

a^{2}

Hard

JEE Advanced

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Light of wavelength $λ_{p h}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $ϕ$ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $λ_{e}$ , which of the following statement(s) is(are) true?

λ_{e}

increases at the same rate as

λ_{p h}

for

λ_{p h} < h c / ϕ

λ_{e}

is approximately halved, if d is doubled

λ_{e}

decreases with increase in

ϕ

and

λ_{p h}

For large potential difference

(V > > ϕ / e) λ_{e}

is approximately halved if V is made four time

Hard

JEE Advanced

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The graph between $1 / λ$ and stopping potential (V) of three metals having work functions $ϕ_{1}, ϕ_{2}$ and $ϕ_{3}$ in an experiment of photo-electric effect is plotted as shown in the figure. Which of the following statement(s) $i s / a r e$ correct? [Here $λ$ is the wavelength of the incident ray].

Ratio of work functions

ϕ_{1}

ϕ_{2}

ϕ_{3} = 1

: 2 : 4

Ratio of work functions

ϕ_{1}

ϕ_{2}

ϕ_{3} = 4

: 2 : 1

tan Θ

is directly proportional to

h c / e

, where

h

is Planck's constant and

c

is the speed of light.

The violet colour light can eject photoelectrons from metals 2 and 3.

Hard

JEE Advanced

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Dual Nature Of Radiation And Matter

Physics 185 Views

A proton has kinetic energy E=100keV which is equal to that of a photon. The wavelength of photon is λ2​ and that of proton is λ1​. The ratio of λ1​/λ2​ is proportional to

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30mWand the speed of light is 3×108m/s. The final momentum of the object is:

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 4 matrix given in the ORS.

An α-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are λα​ and λp​ respectively. The ratio λα​λp​​, to the nearest integer, is:

The speed of the particle that can take discrete values is proportional to

A photon of energy 10.2eV collides inelastically with a Hydrogen atom in ground state. After a certain time interval of few micro seconds another photon of energy 15.0eV collides inelastically with the same hydrogen atom, then the observation made by a suitable detector is

The allowed energy for the particle for a particular value of n is proportional to :

The graph between 1/λ and stopping potential (V) of three metals having work functions ϕ1​, ϕ2​ and ϕ3​ in an experiment of photo-electric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? [Here λ is the wavelength of the incident ray].

Physics
185 Views

A proton has kinetic energy $E = 100 k e V$ which is equal to that of a photon. The wavelength of photon is $λ_{2}$ and that of proton is $λ_{1}$ . The ratio of $λ_{1} / λ_{2}$ is proportional to

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 $m W$ and the speed of light is $3 \times 1 0^{8} m / s$ . The final momentum of the object is:

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and
indicate your answer by darkening appropriate bubbles in the 4 4 matrix given in the ORS.

An $α$ -particle and a proton are accelerated from rest by a potential difference of $100 V$ . After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ respectively. The ratio $\frac{λ _{p}}{λ _{α}}$ , to the nearest integer, is:

A photon of energy $10.2 e V$ collides inelastically with a Hydrogen atom in ground state. After a certain time interval of few micro seconds another photon of energy $15.0 e V$ collides inelastically with the same hydrogen atom, then the observation made by a suitable detector is